commit b8b4747c8edad1a408e5ea7b15108399878ee3db from: Ale date: Sun Feb 1 03:44:51 2026 UTC initial commit commit - 5639813563f93ef0a0bdb84493aa3bc27b80f0ec commit + b8b4747c8edad1a408e5ea7b15108399878ee3db blob - /dev/null blob + b58b603fea78041071d125a30db58d79b3d49217 (mode 644) --- /dev/null +++ .idea/.gitignore @@ -0,0 +1,5 @@ +# Default ignored files +/shelf/ +/workspace.xml +# Editor-based HTTP Client requests +/httpRequests/ blob - /dev/null blob + 01f3f00c6337be60bd04e4ca3b767a11ecddc2e0 (mode 644) --- /dev/null +++ .idea/.name @@ -0,0 +1 @@ +Welcome \ No newline at end of file blob - /dev/null blob + 6f66f972a7640457de4b6ded11ed8e61d6c2661f (mode 644) --- /dev/null +++ .idea/PyCharmMiscProject.iml @@ -0,0 +1,10 @@ + + + + + + + + + + \ No newline at end of file blob - /dev/null blob + 105ce2da2d6447d11dfe32bfb846c3d5b199fc99 (mode 644) --- /dev/null +++ .idea/inspectionProfiles/profiles_settings.xml @@ -0,0 +1,6 @@ + + + + \ No newline at end of file blob - /dev/null blob + 72bda3455512cbf1340b8628cec5c79d95c9287d (mode 644) --- /dev/null +++ .idea/misc.xml @@ -0,0 +1,7 @@ + + + + + + \ No newline at end of file blob - /dev/null blob + f68748e94e65d3c5d6d014f9cf2394f7c1ffa53b (mode 644) --- /dev/null +++ .idea/modules.xml @@ -0,0 +1,8 @@ + + + + + + + + \ No newline at end of file blob - /dev/null blob + 94a25f7f4cb416c083d265558da75d457237d671 (mode 644) --- /dev/null +++ .idea/vcs.xml @@ -0,0 +1,6 @@ + + + + + + \ No newline at end of file blob - /dev/null blob + 556974ac152d456ec9562379f33f6f8f0c3c910e (mode 644) --- /dev/null +++ NoteBooks/.ipynb_checkpoints/Ejercicios_en_clase-checkpoint.ipynb @@ -0,0 +1,1549 @@ +{ + "cells": [ + { + "cell_type": "code", + "id": "5b961fbd-fa2f-4a24-9d18-14b15b196c93", + "metadata": { + "id": "5b961fbd-fa2f-4a24-9d18-14b15b196c93", + "ExecuteTime": { + "end_time": "2026-01-31T18:43:08.670040353Z", + "start_time": "2026-01-31T18:43:08.279132549Z" + } + }, + "source": [ + "import numpy as np\n", + "import sympy as sy\n", + "import matplotlib.pyplot as plt" + ], + "outputs": [], + "execution_count": 1 + }, + { + "cell_type": "markdown", + "id": "8cee1570-fe92-4bc5-8963-3a60940fc99d", + "metadata": { + "id": "8cee1570-fe92-4bc5-8963-3a60940fc99d" + }, + "source": [ + "## 1\n", + "Sean los vectores en $\\mathbb{R}^3$:\n", + "\n", + "$$\\vec{v}_1 = \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix}, \\quad \\vec{v}_2 = \\begin{pmatrix} -2 \\\\ -4 \\\\ 2 \\end{pmatrix}, \\quad \\vec{v}_3 = \\begin{pmatrix} 0 \\\\ 1 \\\\ 1 \\end{pmatrix}$$\n", + "\n", + "1. Sin realizar cálculos exhaustivos, observe la relación entre $\\vec{v}_1$ y $\\vec{v}_2$. ¿Qué implica esta relación sobre el $\\text{span}\\{\\vec{v}_1, \\vec{v}_2\\}$?\n", + "2. Describa geométricamente el subespacio generado por el conjunto $\\{\\vec{v}_1, \\vec{v}_2, \\vec{v}_3\\}$. ¿Es una línea, un plano o todo el espacio $\\mathbb{R}^3$?\n", + "3. Determine si el vector $\\vec{b} = \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 \\end{pmatrix}$ pertenece al $\\text{span}\\{\\vec{v}_1, \\vec{v}_3\\}$. Justifique su respuesta planteando la ecuación vectorial correspondiente.\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2d6c4c6c-14b8-49ad-95f5-ca28eed094b5", + "metadata": { + "id": "2d6c4c6c-14b8-49ad-95f5-ca28eed094b5" + }, + "source": [ + "(Utilizamos *sympy* para realizar cálculos simbólicos con aritmética exacta, lo cuál tiene sentido cuando el número de componentes es pequeño.)\n", + "\n", + "Vamos a definir nuestros vectores." + ] + }, + { + "cell_type": "code", + "id": "75a3c853-3532-41b4-b925-18c30b696ffa", + "metadata": { + "id": "75a3c853-3532-41b4-b925-18c30b696ffa", + "outputId": "d02df2c6-e3ff-4292-cfad-2492a246679d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:08.725145872Z", + "start_time": "2026-01-31T18:43:08.673194042Z" + } + }, + "source": [ + "v1l = [1, 2, -1]\n", + "v2l = [-2, -4, 2]\n", + "v3l = [0, 1, 1]\n", + "\n", + "v1 = sy.Matrix(v1l)\n", + "v2 = sy.Matrix(v2l)\n", + "v3 = sy.Matrix(v3l)\n", + "\n", + "v1" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 1],\n", + "[ 2],\n", + "[-1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1\\\\2\\\\-1\\end{matrix}\\right]$" + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 2 + }, + { + "cell_type": "markdown", + "id": "00f6ce9f-2f2a-4816-9196-fbe1d1f17f12", + "metadata": { + "id": "00f6ce9f-2f2a-4816-9196-fbe1d1f17f12" + }, + "source": [ + "Podemos observar que $$\\vec v_2 = -2 \\vec v_1$$." + ] + }, + { + "cell_type": "code", + "id": "7accffa8-f10f-4532-9cf2-db4845ed8239", + "metadata": { + "id": "7accffa8-f10f-4532-9cf2-db4845ed8239", + "outputId": "ac53bd53-61e1-49fa-e543-bb1f6fbbfed4", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:08.755522723Z", + "start_time": "2026-01-31T18:43:08.738236786Z" + } + }, + "source": [ + "v2 == -2*v1" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 3 + }, + { + "cell_type": "markdown", + "id": "42901511-bce7-46a1-be74-050e0ebac4f9", + "metadata": { + "id": "42901511-bce7-46a1-be74-050e0ebac4f9" + }, + "source": [ + "Luego una combinación lineal arbitraria de estos vectores es igual a un múltiplo de cualquiera de los dos:\n", + "\n", + "$$α v_1 + β v_2 = α v_1 - 2 β v_1 = (α-2β)v_1 .$$\n", + "\n", + "Por lo tanto,\n", + "\n", + "$$spn\\{v_1, v_2\\} = spn\\{v_1\\} = spn\\{v_2\\}.$$\n", + "\n", + "En cuanto a la descripción geométrica del span de los tres vectores, tenemos que debido al resultado anterior\n", + "$$spn\\{v_1, v_2, v_3\\} = spn\\{v_1, v_3\\} = spn\\{v_2, v_3\\}.$$\n", + "Un miembro arbitrario de este conjunto tiene la forma (con $\\alpha, \\beta$ reales arbitrarios)\n", + "$$\\alpha v_1 + \\beta v_3 = \\alpha \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix} + \\beta \\begin{pmatrix} 0 \\\\ 1 \\\\ 1 \\end{pmatrix} = \\begin{pmatrix} \\alpha \\\\ 2\\alpha + \\beta \\\\ \\beta - \\alpha \\end{pmatrix}$$\n", + "\n", + "Claramente, el punto $(0,0,0)$ está incluido en este plano. Vamos a visualizarlo. (Noten que, en Python, las listas están indexadas desde 0 y no desde 1, de modo que v1[0] alude al primer elemento de v1, v1[1] al segundo elemento, etcétera.)" + ] + }, + { + "cell_type": "code", + "id": "39f61e4f-a2c1-4761-b1a1-114b20fb850d", + "metadata": { + "id": "39f61e4f-a2c1-4761-b1a1-114b20fb850d", + "outputId": "da024160-66be-4a72-bbae-ee39603a3314", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 413 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:09.502784637Z", + "start_time": "2026-01-31T18:43:08.774103553Z" + } + }, + "source": [ + "def plot_parametric_plane(point, v1, v2, u_range, v_range):\n", + " \"\"\"\n", + " Plots a plane from its parametric form using matplotlib.\n", + "\n", + " :param point: A numpy array (x0, y0, z0) representing a point on the plane.\n", + " :param v1: A numpy array (a1, b1, c1) representing the first direction vector.\n", + " :param v2: A numpy array (a2, b2, c2) representing the second direction vector.\n", + " :param u_range: A tuple (u_start, u_end, u_steps) for the u parameter.\n", + " :param v_range: A tuple (v_start, v_end, v_steps) for the v parameter.\n", + " \"\"\"\n", + " # Create u and v values\n", + " u = np.linspace(u_range[0], u_range[1], u_range[2])\n", + " v = np.linspace(v_range[0], v_range[1], v_range[2])\n", + "\n", + " # Create a meshgrid for the u and v parameters\n", + " U, V = np.meshgrid(u, v)\n", + "\n", + " # Calculate corresponding x, y, z coordinates using the parametric equation\n", + " # R(u, v) = P0 + u*v1 + v*v2\n", + " X = point[0] + U * v1[0] + V * v2[0]\n", + " Y = point[1] + U * v1[1] + V * v2[1]\n", + " Z = point[2] + U * v1[2] + V * v2[2]\n", + "\n", + " # Plot the surface\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111, projection='3d')\n", + "\n", + " # Use plot_surface for a filled plane or plot_wireframe for a mesh outline\n", + " ax.plot_surface(X, Y, Z, color='red', alpha=0.6)\n", + "\n", + " # Set labels and title\n", + " ax.set_xlabel('eje X')\n", + " ax.set_ylabel('eje Y')\n", + " ax.set_zlabel('eje Z')\n", + "\n", + " # Set axis limits for better visualization if needed\n", + " ax.set_xlim([point[0] - 5, point[0] + 5])\n", + " ax.set_ylim([point[1] - 5, point[1] + 5])\n", + " ax.set_zlim([point[2] - 5, point[2] + 5])\n", + "\n", + " plt.show()\n", + "\n", + "# Define the plane parameters\n", + "point_on_plane = np.array([0, 0, 0])\n", + "vector1 = np.array([1, 2, -1])\n", + "vector2 = np.array([0, 1, 1])\n", + "\n", + "# Define the ranges for parameters u and v\n", + "# (start, end, number of steps)\n", + "u_params = (-5, 5, 50)\n", + "v_params = (-5, 5, 50)\n", + "\n", + "# Call the function to plot the plane\n", + "plot_parametric_plane(point_on_plane, vector1, vector2, u_params, v_params)\n" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
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" + }, + "metadata": {}, + "output_type": "display_data", + "jetTransient": { + "display_id": null + } + } + ], + "execution_count": 4 + }, + { + "cell_type": "markdown", + "id": "fa36f0f9-2c86-4445-8a15-258e28a37246", + "metadata": { + "id": "fa36f0f9-2c86-4445-8a15-258e28a37246" + }, + "source": [ + "Por último, queremos saber si el vector\n", + "$$ \\vec b = \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 \\end{pmatrix}$$\n", + "pertenece al $ spn\\{\\vec v_1, \\vec v_3 \\}$. Para saberlo, planteamos el sistema lineal\n", + "$$ [\\vec v_1 \\vec v_3] \\vec x = \\vec b,$$\n", + "que corresponde a la matriz aumentada\n", + "$$\\left[\\begin{array}{cc|c}1&0&1\\\\2&1&1\\\\-1&1&-3\\end{array}\\right].$$\n" + ] + }, + { + "cell_type": "code", + "id": "8f7324af-7870-479e-8223-89d499ece576", + "metadata": { + "id": "8f7324af-7870-479e-8223-89d499ece576", + "outputId": "e54a6a3a-bc65-4e64-f303-05e8359d0b23", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:09.745640012Z", + "start_time": "2026-01-31T18:43:09.549570123Z" + } + }, + "source": [ + "Al = [[1, 0, 1], [2, 1, 1], [-1, 1, -2]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 1, 0, 1],\n", + "[ 2, 1, 1],\n", + "[-1, 1, -2]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 1\\\\2 & 1 & 1\\\\-1 & 1 & -2\\end{matrix}\\right]$" + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 5 + }, + { + "cell_type": "markdown", + "id": "8d3bdb02-bfad-47e1-9745-55c18046946f", + "metadata": { + "id": "8d3bdb02-bfad-47e1-9745-55c18046946f" + }, + "source": [ + "Vamos a realizar una serie de operaciones elementales por renglón para llevar nuestra matriz a su forma escalonada. Primero, eliminamos los ceros bajo el pivote en la primer columna:" + ] + }, + { + "cell_type": "code", + "id": "e07370f6-823c-4795-92d9-4d4201abd234", + "metadata": { + "id": "e07370f6-823c-4795-92d9-4d4201abd234", + "outputId": "d99fbb64-307f-47c3-ccf8-63fb84a42689", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.053141760Z", + "start_time": "2026-01-31T18:43:09.913846210Z" + } + }, + "source": [ + "A = A.elementary_row_op(\"n->n+km\", row=1, k=-2, row2=0)\n", + "A = A.elementary_row_op(\"n->n+km\", row=2, k=1, row2=0)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 0, 1],\n", + "[0, 1, -1],\n", + "[0, 1, -1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 1\\\\0 & 1 & -1\\\\0 & 1 & -1\\end{matrix}\\right]$" + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 6 + }, + { + "cell_type": "markdown", + "id": "0e3b1eed-bb1f-42f3-8c66-d33a00570c90", + "metadata": { + "id": "0e3b1eed-bb1f-42f3-8c66-d33a00570c90" + }, + "source": [ + "Luego, eliminamos los ceros bajo el pivote en la segunda columna:" + ] + }, + { + "cell_type": "code", + "id": "7082a07a-f4c5-485a-b666-1f22e6474d58", + "metadata": { + "id": "7082a07a-f4c5-485a-b666-1f22e6474d58", + "outputId": "a6fb420e-2f03-4fb7-987c-e90466bccf80", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.157696692Z", + "start_time": "2026-01-31T18:43:10.089302515Z" + } + }, + "source": [ + "A = A.elementary_row_op(\"n->n+km\", row=2, k=-1, row2=1)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 0, 1],\n", + "[0, 1, -1],\n", + "[0, 0, 0]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 1\\\\0 & 1 & -1\\\\0 & 0 & 0\\end{matrix}\\right]$" + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 7 + }, + { + "cell_type": "markdown", + "id": "ce2ed12b-996a-431c-96f8-51157b44385e", + "metadata": { + "id": "ce2ed12b-996a-431c-96f8-51157b44385e" + }, + "source": [ + "En este punto, tenemos la respuesta: este sistema no es inconsistente y por lo tanto $\\vec b \\in {spn}\\{\\vec v_1, \\vec v_3 \\}$. Pero además nuestra matriz está en forma escalonada reducida, y por tanto tenemos la solución al sistema:\n", + "\n", + "$$\\vec v_1 - \\vec v_3 = \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix} - \\begin{pmatrix} 0 \\\\ 1 \\\\ 1 \\end{pmatrix} = \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 \\end{pmatrix} = \\vec b.$$" + ] + }, + { + "cell_type": "markdown", + "id": "99e9cf6c-8e59-4c1f-9f5c-f668c4dba885", + "metadata": { + "id": "99e9cf6c-8e59-4c1f-9f5c-f668c4dba885" + }, + "source": [ + "## 2\n", + "Considere el siguiente sistema de ecuaciones lineales dependiente de un parámetro $h \\in \\mathbb{R}$:\n", + "\n", + "$$\\begin{aligned}\n", + "x_1 + hx_2 &= 2 \\\\\n", + "4x_1 + 8x_2 &= 8\n", + "\\end{aligned}$$\n", + "\n", + "1. Escriba la matriz aumentada $[A | \\vec{b}]$ y aplique operaciones elementales de fila para llevarla a su forma escalonada (REF).\n", + "2. Encuentre el valor específico de $h$ para el cual el sistema posee **infinitas soluciones**.\n", + "3. Para el valor de $h$ hallado en el inciso anterior, escriba el conjunto solución en **forma vectorial paramétrica**: $$\\vec{x} = \\vec{p} + t\\vec{v}_h$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "ef3ef9b9-5488-4890-a034-794db338e9b6", + "metadata": { + "id": "ef3ef9b9-5488-4890-a034-794db338e9b6" + }, + "source": [ + "En este caso, la matriz aumentada es\n", + "$$A=\\left[\\begin{array}{cc|c}1&h&2\\\\4&8&8\\end{array}\\right].$$\n" + ] + }, + { + "cell_type": "code", + "id": "dfebd2fb-66d4-4576-9097-425d64420c22", + "metadata": { + "id": "dfebd2fb-66d4-4576-9097-425d64420c22", + "outputId": "838030ba-171c-46bb-9e88-337dc39af120", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.195401554Z", + "start_time": "2026-01-31T18:43:10.161100983Z" + } + }, + "source": [ + "h = sy.symbols('h')\n", + "Al = [[1,h,2],[4,8,8]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, h, 2],\n", + "[4, 8, 8]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & h & 2\\\\4 & 8 & 8\\end{matrix}\\right]$" + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 8 + }, + { + "cell_type": "markdown", + "id": "f2300fde-a9e8-4d56-9aec-ebdf7c2f3137", + "metadata": { + "id": "f2300fde-a9e8-4d56-9aec-ebdf7c2f3137" + }, + "source": [ + "La forma escalonada de esta matriz es" + ] + }, + { + "cell_type": "code", + "id": "627658f9-7297-4a13-b087-93571fdc81a4", + "metadata": { + "id": "627658f9-7297-4a13-b087-93571fdc81a4", + "outputId": "251aab4e-b442-425c-b822-6681b9200b72", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.361825919Z", + "start_time": "2026-01-31T18:43:10.197993833Z" + } + }, + "source": [ + "A.echelon_form()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, h, 2],\n", + "[0, 8 - 4*h, 0]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & h & 2\\\\0 & 8 - 4 h & 0\\end{matrix}\\right]$" + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 9 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "De aquí podemos concluir que el sistema es inconsistente cuando\n", + "$$ 8-4h = 0 \\Rightarrow h = 2$$\n", + "y la constante en el lado derecho es distinta de cero. Pero observemos la segunda fila completa: $0x_1 + 0x_2 = 0$ cuando $h=2$.\n", + "Por el contrario, cuando\n", + "$$ 8-4h = 0 \\Rightarrow h = 2, $$\n", + "el sistema tiene soluciones infinitas, dado que tenemos un renglón de ceros y tenemos una ecuación para dos variables." + ], + "id": "ef1a82ca9510fe2e" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.458225618Z", + "start_time": "2026-01-31T18:43:10.394971538Z" + } + }, + "cell_type": "code", + "source": "A.subs(h,2).echelon_form()", + "id": "fb4874e4a0566dbe", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2, 2],\n", + "[0, 0, 0]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2 & 2\\\\0 & 0 & 0\\end{matrix}\\right]$" + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 10 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "¿Cómo encontramos la forma paramétrica de esta solución? Sabemos que\n", + "\n", + "$$x_1 + 2 x_2 = 2 \\Rightarrow x_2 = 1 - \\frac{x_1}{2}.$$\n", + "Luego, en términos de un parámetro $t$, la solución tiene la forma \n", + "$$ \\vec x = \\begin{pmatrix}t \\\\ 1 - \\frac{t}{2} \\end{pmatrix} = \\begin{pmatrix}0\\\\ 1 \\end{pmatrix} + t \\begin{pmatrix}1 \\\\ -1/2 \\end{pmatrix}.$$\n", + "El primer vector corresponde a la *solución particular*, es decir, $x_1=0, x_2 = 1$ resuelven el problema original con $h=2$, mientras que el segundo vector representa una *solución homogénea*: si $x_1$ es cualquier valor $t$, y $x_2 = 1- t/2$, tenemos una solución al sistema original con $\\vec b = 0$.\n", + "\n" + ], + "id": "e1dccbcc50bcca06" + }, + { + "cell_type": "markdown", + "id": "9a6b5985-b380-421b-8c20-f5c5cf2bed5a", + "metadata": { + "id": "9a6b5985-b380-421b-8c20-f5c5cf2bed5a" + }, + "source": [ + "## 3\n", + "Sea la matriz $A$ y el vector de pesos $\\vec{x}$:\n", + "\n", + "$$A = \\begin{pmatrix} 1 & 5 & -2 \\\\ -3 & 0 & 1 \\end{pmatrix}, \\quad \\vec{x} = \\begin{pmatrix} 2 \\\\ 1 \\\\ 4 \\end{pmatrix}$$\n", + "\n", + "1. Calcule el producto $A\\vec{x}$ utilizando **exclusivamente** la definición de combinación lineal de las columnas de $A$:\n", + " $$x_1\\vec{a}_1 + x_2\\vec{a}_2 + x_3\\vec{a}_3 = \\vec{b}$$\n", + "2. Si se sabe que la ecuación $A\\vec{x} = \\vec{0}$ admite una solución no trivial $\\vec{x} = \\begin{pmatrix} 1 \\\\ 1 \\\\ 2 \\end{pmatrix}$, ¿qué podemos afirmar sobre las columnas de $A$?" + ] + }, + { + "cell_type": "code", + "id": "ce28cb87-dcde-4b5b-bba0-2fc6e632e679", + "metadata": { + "id": "ce28cb87-dcde-4b5b-bba0-2fc6e632e679", + "outputId": "d57bbe0a-62d0-433a-86e0-771ee999ecde", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.551258903Z", + "start_time": "2026-01-31T18:43:10.462669308Z" + } + }, + "source": [ + "Al = [[1,5,-2],[-3,0,1]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 1, 5, -2],\n", + "[-3, 0, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 5 & -2\\\\-3 & 0 & 1\\end{matrix}\\right]$" + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 11 + }, + { + "cell_type": "code", + "id": "8482c529-15cd-47ad-9d97-96c8e6a8a03a", + "metadata": { + "id": "8482c529-15cd-47ad-9d97-96c8e6a8a03a", + "outputId": "c9220c19-04e4-4b98-ed22-6a36894d59a7", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.596586744Z", + "start_time": "2026-01-31T18:43:10.562581863Z" + } + }, + "source": [ + "xl = [2,1,4]\n", + "x = sy.Matrix(xl)\n", + "x\n" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[2],\n", + "[1],\n", + "[4]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}2\\\\1\\\\4\\end{matrix}\\right]$" + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 12 + }, + { + "cell_type": "markdown", + "id": "a8b64d5f-f869-495a-be01-eb10482078b8", + "metadata": { + "id": "a8b64d5f-f869-495a-be01-eb10482078b8" + }, + "source": [ + "Vamos a calcular la combinación lineal:" + ] + }, + { + "cell_type": "code", + "id": "bdafd480-49e8-43a1-8b9f-f7cd863cd39f", + "metadata": { + "id": "bdafd480-49e8-43a1-8b9f-f7cd863cd39f", + "outputId": "15a6923b-9551-459f-bed5-5c7a66055b56", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.641194892Z", + "start_time": "2026-01-31T18:43:10.604208176Z" + } + }, + "source": [ + "x[0]*A[:,0] + x[1]*A[:,1] + x[2]*A[:,2]" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[-1],\n", + "[-2]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1\\\\-2\\end{matrix}\\right]$" + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 13 + }, + { + "cell_type": "code", + "id": "f20304f9-8806-4863-96bd-c89b20d60c42", + "metadata": { + "id": "f20304f9-8806-4863-96bd-c89b20d60c42", + "outputId": "95176e65-de1b-41c2-c858-b12e56629a0d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.679145718Z", + "start_time": "2026-01-31T18:43:10.647324937Z" + } + }, + "source": [ + "A*x" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[-1],\n", + "[-2]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1\\\\-2\\end{matrix}\\right]$" + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 14 + }, + { + "cell_type": "markdown", + "id": "e2166405-28cc-4697-ab33-bb864fd54e88", + "metadata": { + "id": "e2166405-28cc-4697-ab33-bb864fd54e88" + }, + "source": [ + "Se nos da una solución al problema $A\\vec x = 0$:\n", + "$$\\vec x = \\begin{pmatrix} 1\\\\ 1 \\\\ 2\\end{pmatrix}.$$\n", + "Esto significa que, si denotamos las columnas de A como $\\vec a_1, \\vec a_2, \\vec a_3$, la combinación\n", + "$$\\vec a_1 + \\vec a_2 + 2 \\vec a_3 = 0 $$" + ] + }, + { + "cell_type": "code", + "id": "ad3600aa-abd6-4022-bf98-08e3608a243c", + "metadata": { + "id": "ad3600aa-abd6-4022-bf98-08e3608a243c", + "outputId": "55faf3e6-8bc9-43e5-d927-9eacbe07d12d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.723848286Z", + "start_time": "2026-01-31T18:43:10.682499513Z" + } + }, + "source": "A[:,0] + A[:,1] + 2*A[:,2]", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 2],\n", + "[-1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}2\\\\-1\\end{matrix}\\right]$" + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 15 + }, + { + "cell_type": "markdown", + "id": "b1a8e840-fed8-4df2-b9f2-3237d4d86291", + "metadata": { + "id": "b1a8e840-fed8-4df2-b9f2-3237d4d86291" + }, + "source": [ + "\n", + "Por lo tanto, uno de estos vectores puede reescribirse en términos de los otros. Por ejemplo:\n", + "$$ \\vec a_2 = -\\vec a_1 - 2\\vec a_3$$\n" + ] + }, + { + "cell_type": "code", + "id": "248282cb-699e-41b5-a248-7cdd21534024", + "metadata": { + "id": "248282cb-699e-41b5-a248-7cdd21534024", + "outputId": "79c3bf72-f0e0-44be-d50f-0d47df4581d1", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.773915764Z", + "start_time": "2026-01-31T18:43:10.738755729Z" + } + }, + "source": "A[:,1] == -A[:,0] - 2*A[:,2]", + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 16 + }, + { + "cell_type": "markdown", + "id": "c90d490f-efb6-4f6e-84a6-d07519b23c33", + "metadata": { + "id": "c90d490f-efb6-4f6e-84a6-d07519b23c33" + }, + "source": [ + "Luego entonces,\n", + "\n", + "$$\\text{span}\\{\\vec a_1,\\vec a_2,\\vec a_3\\}=\\text{span}\\{\\vec a_1,\\vec a_3\\}.$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1f796754-7393-4376-b875-c41165b7d5b4", + "metadata": { + "id": "1f796754-7393-4376-b875-c41165b7d5b4" + }, + "source": [ + "## 4\n", + "Dadas las siguientes matrices de \"cizallamiento\":\n", + "\n", + "$$A = \\begin{pmatrix} 1 & 2 \\\\ 0 & 1 \\end{pmatrix}, \\quad B = \\begin{pmatrix} 1 & 0 \\\\ 2 & 1 \\end{pmatrix}$$\n", + "\n", + "1. Calcule los productos $AB$ y $BA$. Demuestre explícitamente que $AB \\neq BA$.\n", + "2. Si $A$ representa una deformación horizontal y $B$ una deformación vertical, ¿por qué el estado final del sistema depende del orden en que se aplican estas deformaciones?\n", + "3. Calcule $(AB)^T$ y verifique numéricamente la identidad fundamental:\n", + " $$(AB)^T = B^T A^T$$" + ] + }, + { + "cell_type": "markdown", + "id": "1dd12102-54c6-4a9e-bc58-5094a06be49d", + "metadata": { + "id": "1dd12102-54c6-4a9e-bc58-5094a06be49d" + }, + "source": [ + "Definimos nuestras matrices:" + ] + }, + { + "cell_type": "code", + "id": "c5e06ea9-146e-4335-82df-ad2f9db5ea76", + "metadata": { + "id": "c5e06ea9-146e-4335-82df-ad2f9db5ea76", + "outputId": "70eca042-0241-4c08-e1fd-b4113991a08c", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.843697057Z", + "start_time": "2026-01-31T18:43:10.796542885Z" + } + }, + "source": [ + "Al = [[1,2],[0,1]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2],\n", + "[0, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\0 & 1\\end{matrix}\\right]$" + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 17 + }, + { + "cell_type": "code", + "id": "14e27cb3-47e9-4448-87ac-05248c548698", + "metadata": { + "id": "14e27cb3-47e9-4448-87ac-05248c548698", + "outputId": "32c819f5-88cc-4383-fda3-8f27fc2d28e2", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.878178417Z", + "start_time": "2026-01-31T18:43:10.846024746Z" + } + }, + "source": [ + "Bl = [[1,0],[2,1]]\n", + "B = sy.Matrix(Bl)\n", + "B" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 0],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 18 + }, + { + "cell_type": "markdown", + "id": "5f5cb42a-7ca7-4205-8658-1c3a88336952", + "metadata": { + "id": "5f5cb42a-7ca7-4205-8658-1c3a88336952" + }, + "source": [ + "Evaluamos los productos:" + ] + }, + { + "cell_type": "code", + "id": "2dff8d1b-68b8-4727-ab55-5731b0e08ce3", + "metadata": { + "id": "2dff8d1b-68b8-4727-ab55-5731b0e08ce3", + "outputId": "c4534ee7-b84c-4e0e-e726-ace07489e41e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.929300959Z", + "start_time": "2026-01-31T18:43:10.894990384Z" + } + }, + "source": [ + "A*B" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[5, 2],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}5 & 2\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 19 + }, + { + "cell_type": "code", + "id": "c7646525-8450-475c-b042-0956b0e5761f", + "metadata": { + "id": "c7646525-8450-475c-b042-0956b0e5761f", + "outputId": "508f1417-90b9-45f0-a9fa-fbee297c6994", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.967053376Z", + "start_time": "2026-01-31T18:43:10.931822104Z" + } + }, + "source": [ + "B*A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2],\n", + "[2, 5]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\2 & 5\\end{matrix}\\right]$" + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 20 + }, + { + "cell_type": "markdown", + "id": "9d2a201d-6a1c-42a1-b8c5-573a36298292", + "metadata": { + "id": "9d2a201d-6a1c-42a1-b8c5-573a36298292" + }, + "source": [ + "Claramente, $AB\\neq BA$:" + ] + }, + { + "cell_type": "code", + "id": "31cfb6dc-1849-42e3-8cc3-af75e0e1ac87", + "metadata": { + "id": "31cfb6dc-1849-42e3-8cc3-af75e0e1ac87", + "outputId": "435d2352-a7ab-4cb2-8178-a5996c290929", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.041116648Z", + "start_time": "2026-01-31T18:43:10.981263839Z" + } + }, + "source": [ + "A*B == B*A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 21 + }, + { + "cell_type": "markdown", + "id": "74675073-b17c-4f99-8196-496fe0c8dbdc", + "metadata": { + "id": "74675073-b17c-4f99-8196-496fe0c8dbdc" + }, + "source": [ + "Para clarificar el efecto de estas matrices, consideremos el triángulo con vértices en los puntos $(-1,0), (1,0)$, y $(0,2)$. Vamos a ver el efecto de aplicar AB y BA a estos puntos:" + ] + }, + { + "cell_type": "code", + "id": "1516a3a0-4d64-4493-aad8-a3240ad67dd0", + "metadata": { + "id": "1516a3a0-4d64-4493-aad8-a3240ad67dd0", + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.116280767Z", + "start_time": "2026-01-31T18:43:11.075949739Z" + } + }, + "source": [ + "vert = [[-1, 0], [0,2], [1, 0]]\n", + "ABvert=[(A*B*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "BAvert=[(B*A*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "ABvertices = np.array(ABvert)\n", + "BAvertices = np.array(BAvert)\n" + ], + "outputs": [], + "execution_count": 22 + }, + { + "cell_type": "markdown", + "id": "ea868e22-9bdb-4e9b-9a87-1d94c0e4b68a", + "metadata": { + "id": "ea868e22-9bdb-4e9b-9a87-1d94c0e4b68a" + }, + "source": [ + "Al aplicar AB, terminamos con un triángulo con vértices en los puntos $(-5,-2), (4,2)$ y $(5,2)$." + ] + }, + { + "cell_type": "code", + "id": "9d930e3a-40c9-4277-a77a-b9b46a8f5a29", + "metadata": { + "id": "9d930e3a-40c9-4277-a77a-b9b46a8f5a29", + "outputId": "2a72c25f-702d-4be9-82a0-2fd3306e3d70", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.184756752Z", + "start_time": "2026-01-31T18:43:11.119226145Z" + } + }, + "source": [ + "ABvert" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "[[-5, -2], [4, 2], [5, 2]]" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 23 + }, + { + "cell_type": "markdown", + "id": "7f37c8a0-909f-4e6b-8299-03b832673bc8", + "metadata": { + "id": "7f37c8a0-909f-4e6b-8299-03b832673bc8" + }, + "source": "Al aplicar BA, terminamos con un triángulo con vértices en los puntos $(-1,-2), (4,6)$ y $(1,2)$. ¡Estos son triángulos muy diferentes!" + }, + { + "cell_type": "code", + "id": "4b7a8ea1-2bc5-4ae2-8e9a-ce2face0c759", + "metadata": { + "id": "4b7a8ea1-2bc5-4ae2-8e9a-ce2face0c759", + "outputId": "91b61957-54f3-40df-e250-bc40537a6c90", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.228580539Z", + "start_time": "2026-01-31T18:43:11.197151857Z" + } + }, + "source": [ + "BAvert" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "[[-1, -2], [4, 10], [1, 2]]" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 24 + }, + { + "cell_type": "markdown", + "id": "67c4c8a9-22b2-41a6-81ca-729d124a73d1", + "metadata": { + "id": "67c4c8a9-22b2-41a6-81ca-729d124a73d1" + }, + "source": [ + "Vamos a visualizarlos. En azul está en triángulo original, en rojo el triángulo al que aplicamos AB, y en verde al que aplicamos BA." + ] + }, + { + "cell_type": "code", + "id": "d9e5e256-1412-4d3d-ad2f-89326b29e788", + "metadata": { + "id": "d9e5e256-1412-4d3d-ad2f-89326b29e788", + "outputId": "03f2016a-0fb0-4a6e-f7c2-d0470d719d31", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.348724945Z", + "start_time": "2026-01-31T18:43:11.234649509Z" + } + }, + "source": [ + "from matplotlib.patches import Polygon\n", + "from matplotlib.path import Path\n", + "from matplotlib.patches import PathPatch\n", + "\n", + "# Define the vertices of the triangle (x, y coordinates)\n", + "# Example: an arbitrary triangle with 3 points\n", + "vertices = np.array(vert)\n", + "\n", + "# Create a figure and an axes\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Create a Polygon patch\n", + "# facecolor='blue' fills the triangle, edgecolor='black' adds an outline\n", + "triangle = Polygon(vertices, closed=True, facecolor='blue', edgecolor='black')\n", + "ABtriangle = Polygon(ABvertices, closed=True, facecolor='red', edgecolor='black')\n", + "BAtriangle = Polygon(BAvertices, closed=True, facecolor='green', edgecolor='black')\n", + "\n", + "# Add the patch to the axes\n", + "ax.add_patch(triangle)\n", + "ax.add_patch(ABtriangle)\n", + "ax.add_patch(BAtriangle)\n", + "\n", + "# Set the axis limits for better viewing\n", + "ax.set_xlim(-5.5, 5.5)\n", + "ax.set_ylim(-2.5, 10.5)\n", + "ax.set_aspect('equal', adjustable='box') # Ensures the triangle isn't stretched\n", + "\n", + "# Add labels and a title\n", + "#plt.xlabel('X-axis')\n", + "#plt.ylabel('Y-axis')\n", + "#plt.title('Triangle drawn with Matplotlib')\n", + "#plt.grid(True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data", + "jetTransient": { + "display_id": null + } + } + ], + "execution_count": 25 + }, + { + "cell_type": "markdown", + "id": "f854f28a-826c-4dc0-a080-a203664a76f6", + "metadata": { + "id": "f854f28a-826c-4dc0-a080-a203664a76f6" + }, + "source": [ + "Podemos visualizarlo mejor si utilizamos una deformación más pequeña." + ] + }, + { + "cell_type": "code", + "id": "660e17c9-88c9-435e-b606-9b25044f304b", + "metadata": { + "id": "660e17c9-88c9-435e-b606-9b25044f304b", + "outputId": "26e068aa-9bc5-4d0d-dc27-b87e9c8ef675", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.568243361Z", + "start_time": "2026-01-31T18:43:11.374055939Z" + } + }, + "source": [ + "Al2 = [[1,1.1],[0,1]]\n", + "A2 = sy.Matrix(Al2)\n", + "Bl2 = [[1,0],[1.1,1]]\n", + "B2 = sy.Matrix(Bl2)\n", + "vert = [[-1, 0], [0,2], [1, 0]]\n", + "ABvert2=[(A2*B2*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "BAvert2=[(B2*A2*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "ABvertices2 = np.array(ABvert2)\n", + "BAvertices2 = np.array(BAvert2)\n", + "\n", + "\n", + "# Define the vertices of the triangle (x, y coordinates)\n", + "# Example: an arbitrary triangle with 3 points\n", + "vertices = np.array(vert)\n", + "\n", + "# Create a figure and an axes\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Create a Polygon patch\n", + "# facecolor='blue' fills the triangle, edgecolor='black' adds an outline\n", + "triangle = Polygon(vertices, closed=True, facecolor='blue', edgecolor='black')\n", + "ABtriangle2 = Polygon(ABvertices2, closed=True, facecolor='red', edgecolor='black')\n", + "BAtriangle2 = Polygon(BAvertices2, closed=True, facecolor='green', edgecolor='black')\n", + "\n", + "# Add the patch to the axes\n", + "ax.add_patch(triangle)\n", + "ax.add_patch(ABtriangle2)\n", + "ax.add_patch(BAtriangle2)\n", + "\n", + "# Set the axis limits for better viewing\n", + "ax.set_xlim(-2.5, 2.5)\n", + "ax.set_ylim(-2.5, 5.5)\n", + "ax.set_aspect('equal', adjustable='box') # Ensures the triangle isn't stretched\n", + "\n", + "# Add labels and a title\n", + "#plt.xlabel('X-axis')\n", + "#plt.ylabel('Y-axis')\n", + "#plt.title('Triangle drawn with Matplotlib')\n", + "#plt.grid(True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data", + "jetTransient": { + "display_id": null + } + } + ], + "execution_count": 26 + }, + { + "cell_type": "markdown", + "id": "ecac7d27-6a72-40ec-a762-b03ef6ca3175", + "metadata": { + "id": "ecac7d27-6a72-40ec-a762-b03ef6ca3175" + }, + "source": [ + "Sólo nos resta evaluar las matrices transpuestas. En el caso de $(AB)^T$, tenemos que\n", + "\n", + "$$(AB)^T = \\begin{pmatrix} 5 & 2 \\\\ 2 & 1\\end{pmatrix}.$$\n" + ] + }, + { + "cell_type": "code", + "id": "83dd6160-8679-4849-98d6-2be1da2ec3a5", + "metadata": { + "id": "83dd6160-8679-4849-98d6-2be1da2ec3a5", + "outputId": "8ed6d146-12b5-459a-bccc-ac0ea616f429", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.617142273Z", + "start_time": "2026-01-31T18:43:11.586161077Z" + } + }, + "source": [ + "(A*B).T" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[5, 2],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}5 & 2\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 27 + }, + { + "cell_type": "markdown", + "id": "8cc29772-781d-46b9-9af1-20d4e20cdfab", + "metadata": { + "id": "8cc29772-781d-46b9-9af1-20d4e20cdfab" + }, + "source": [ + "Por otra parte,\n", + "\n", + "$$B^T A^T = \\begin{pmatrix} 5 & 2 \\\\ 2 & 1\\end{pmatrix}.$$" + ] + }, + { + "cell_type": "code", + "id": "285b5969-0f95-46ec-bdc3-b1668122c7f9", + "metadata": { + "id": "285b5969-0f95-46ec-bdc3-b1668122c7f9", + "outputId": "a8eb1df4-54f0-41a1-b503-2bdd0b100d5f", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.658001287Z", + "start_time": "2026-01-31T18:43:11.625961336Z" + } + }, + "source": "B.T*A.T", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[5, 2],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}5 & 2\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 28 + }, + { + "cell_type": "markdown", + "id": "65ce9599-42fe-4d90-bc0b-58efc29670d6", + "metadata": { + "id": "65ce9599-42fe-4d90-bc0b-58efc29670d6" + }, + "source": [ + "mientras que\n", + "$$A^T B^T = \\begin{pmatrix} 1 & 2 \\\\ 2 & 5\\end{pmatrix}.$$\n" + ] + }, + { + "cell_type": "code", + "id": "374a319d-1f40-4c81-a03e-ba86cb5d86cc", + "metadata": { + "id": "374a319d-1f40-4c81-a03e-ba86cb5d86cc", + "outputId": "8d5bc463-9e46-4dba-8eea-191f61ab8b40", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.690909502Z", + "start_time": "2026-01-31T18:43:11.660057451Z" + } + }, + "source": "A.T*B.T\n", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2],\n", + "[2, 5]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\2 & 5\\end{matrix}\\right]$" + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 29 + }, + { + "cell_type": "markdown", + "id": "ccb66e03-3ad0-4a3e-819a-4d78f210f9de", + "metadata": { + "id": "ccb66e03-3ad0-4a3e-819a-4d78f210f9de" + }, + "source": [ + "Entonces," + ] + }, + { + "cell_type": "code", + "id": "01af621c-14ec-4e45-ac16-29c93acad923", + "metadata": { + "id": "01af621c-14ec-4e45-ac16-29c93acad923", + "outputId": "15631aec-0a72-4163-e9a4-86706ba48152", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.724827772Z", + "start_time": "2026-01-31T18:43:11.696040095Z" + } + }, + "source": [ + "(A*B).T == B.T*A.T" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 30 + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + }, + "colab": { + "provenance": [] + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} blob - /dev/null blob + 556974ac152d456ec9562379f33f6f8f0c3c910e (mode 644) --- /dev/null +++ NoteBooks/Ejercicios_en_clase.ipynb @@ -0,0 +1,1549 @@ +{ + "cells": [ + { + "cell_type": "code", + "id": "5b961fbd-fa2f-4a24-9d18-14b15b196c93", + "metadata": { + "id": "5b961fbd-fa2f-4a24-9d18-14b15b196c93", + "ExecuteTime": { + "end_time": "2026-01-31T18:43:08.670040353Z", + "start_time": "2026-01-31T18:43:08.279132549Z" + } + }, + "source": [ + "import numpy as np\n", + "import sympy as sy\n", + "import matplotlib.pyplot as plt" + ], + "outputs": [], + "execution_count": 1 + }, + { + "cell_type": "markdown", + "id": "8cee1570-fe92-4bc5-8963-3a60940fc99d", + "metadata": { + "id": "8cee1570-fe92-4bc5-8963-3a60940fc99d" + }, + "source": [ + "## 1\n", + "Sean los vectores en $\\mathbb{R}^3$:\n", + "\n", + "$$\\vec{v}_1 = \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix}, \\quad \\vec{v}_2 = \\begin{pmatrix} -2 \\\\ -4 \\\\ 2 \\end{pmatrix}, \\quad \\vec{v}_3 = \\begin{pmatrix} 0 \\\\ 1 \\\\ 1 \\end{pmatrix}$$\n", + "\n", + "1. Sin realizar cálculos exhaustivos, observe la relación entre $\\vec{v}_1$ y $\\vec{v}_2$. ¿Qué implica esta relación sobre el $\\text{span}\\{\\vec{v}_1, \\vec{v}_2\\}$?\n", + "2. Describa geométricamente el subespacio generado por el conjunto $\\{\\vec{v}_1, \\vec{v}_2, \\vec{v}_3\\}$. ¿Es una línea, un plano o todo el espacio $\\mathbb{R}^3$?\n", + "3. Determine si el vector $\\vec{b} = \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 \\end{pmatrix}$ pertenece al $\\text{span}\\{\\vec{v}_1, \\vec{v}_3\\}$. Justifique su respuesta planteando la ecuación vectorial correspondiente.\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "2d6c4c6c-14b8-49ad-95f5-ca28eed094b5", + "metadata": { + "id": "2d6c4c6c-14b8-49ad-95f5-ca28eed094b5" + }, + "source": [ + "(Utilizamos *sympy* para realizar cálculos simbólicos con aritmética exacta, lo cuál tiene sentido cuando el número de componentes es pequeño.)\n", + "\n", + "Vamos a definir nuestros vectores." + ] + }, + { + "cell_type": "code", + "id": "75a3c853-3532-41b4-b925-18c30b696ffa", + "metadata": { + "id": "75a3c853-3532-41b4-b925-18c30b696ffa", + "outputId": "d02df2c6-e3ff-4292-cfad-2492a246679d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:08.725145872Z", + "start_time": "2026-01-31T18:43:08.673194042Z" + } + }, + "source": [ + "v1l = [1, 2, -1]\n", + "v2l = [-2, -4, 2]\n", + "v3l = [0, 1, 1]\n", + "\n", + "v1 = sy.Matrix(v1l)\n", + "v2 = sy.Matrix(v2l)\n", + "v3 = sy.Matrix(v3l)\n", + "\n", + "v1" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 1],\n", + "[ 2],\n", + "[-1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1\\\\2\\\\-1\\end{matrix}\\right]$" + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 2 + }, + { + "cell_type": "markdown", + "id": "00f6ce9f-2f2a-4816-9196-fbe1d1f17f12", + "metadata": { + "id": "00f6ce9f-2f2a-4816-9196-fbe1d1f17f12" + }, + "source": [ + "Podemos observar que $$\\vec v_2 = -2 \\vec v_1$$." + ] + }, + { + "cell_type": "code", + "id": "7accffa8-f10f-4532-9cf2-db4845ed8239", + "metadata": { + "id": "7accffa8-f10f-4532-9cf2-db4845ed8239", + "outputId": "ac53bd53-61e1-49fa-e543-bb1f6fbbfed4", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:08.755522723Z", + "start_time": "2026-01-31T18:43:08.738236786Z" + } + }, + "source": [ + "v2 == -2*v1" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 3 + }, + { + "cell_type": "markdown", + "id": "42901511-bce7-46a1-be74-050e0ebac4f9", + "metadata": { + "id": "42901511-bce7-46a1-be74-050e0ebac4f9" + }, + "source": [ + "Luego una combinación lineal arbitraria de estos vectores es igual a un múltiplo de cualquiera de los dos:\n", + "\n", + "$$α v_1 + β v_2 = α v_1 - 2 β v_1 = (α-2β)v_1 .$$\n", + "\n", + "Por lo tanto,\n", + "\n", + "$$spn\\{v_1, v_2\\} = spn\\{v_1\\} = spn\\{v_2\\}.$$\n", + "\n", + "En cuanto a la descripción geométrica del span de los tres vectores, tenemos que debido al resultado anterior\n", + "$$spn\\{v_1, v_2, v_3\\} = spn\\{v_1, v_3\\} = spn\\{v_2, v_3\\}.$$\n", + "Un miembro arbitrario de este conjunto tiene la forma (con $\\alpha, \\beta$ reales arbitrarios)\n", + "$$\\alpha v_1 + \\beta v_3 = \\alpha \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix} + \\beta \\begin{pmatrix} 0 \\\\ 1 \\\\ 1 \\end{pmatrix} = \\begin{pmatrix} \\alpha \\\\ 2\\alpha + \\beta \\\\ \\beta - \\alpha \\end{pmatrix}$$\n", + "\n", + "Claramente, el punto $(0,0,0)$ está incluido en este plano. Vamos a visualizarlo. (Noten que, en Python, las listas están indexadas desde 0 y no desde 1, de modo que v1[0] alude al primer elemento de v1, v1[1] al segundo elemento, etcétera.)" + ] + }, + { + "cell_type": "code", + "id": "39f61e4f-a2c1-4761-b1a1-114b20fb850d", + "metadata": { + "id": "39f61e4f-a2c1-4761-b1a1-114b20fb850d", + "outputId": "da024160-66be-4a72-bbae-ee39603a3314", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 413 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:09.502784637Z", + "start_time": "2026-01-31T18:43:08.774103553Z" + } + }, + "source": [ + "def plot_parametric_plane(point, v1, v2, u_range, v_range):\n", + " \"\"\"\n", + " Plots a plane from its parametric form using matplotlib.\n", + "\n", + " :param point: A numpy array (x0, y0, z0) representing a point on the plane.\n", + " :param v1: A numpy array (a1, b1, c1) representing the first direction vector.\n", + " :param v2: A numpy array (a2, b2, c2) representing the second direction vector.\n", + " :param u_range: A tuple (u_start, u_end, u_steps) for the u parameter.\n", + " :param v_range: A tuple (v_start, v_end, v_steps) for the v parameter.\n", + " \"\"\"\n", + " # Create u and v values\n", + " u = np.linspace(u_range[0], u_range[1], u_range[2])\n", + " v = np.linspace(v_range[0], v_range[1], v_range[2])\n", + "\n", + " # Create a meshgrid for the u and v parameters\n", + " U, V = np.meshgrid(u, v)\n", + "\n", + " # Calculate corresponding x, y, z coordinates using the parametric equation\n", + " # R(u, v) = P0 + u*v1 + v*v2\n", + " X = point[0] + U * v1[0] + V * v2[0]\n", + " Y = point[1] + U * v1[1] + V * v2[1]\n", + " Z = point[2] + U * v1[2] + V * v2[2]\n", + "\n", + " # Plot the surface\n", + " fig = plt.figure()\n", + " ax = fig.add_subplot(111, projection='3d')\n", + "\n", + " # Use plot_surface for a filled plane or plot_wireframe for a mesh outline\n", + " ax.plot_surface(X, Y, Z, color='red', alpha=0.6)\n", + "\n", + " # Set labels and title\n", + " ax.set_xlabel('eje X')\n", + " ax.set_ylabel('eje Y')\n", + " ax.set_zlabel('eje Z')\n", + "\n", + " # Set axis limits for better visualization if needed\n", + " ax.set_xlim([point[0] - 5, point[0] + 5])\n", + " ax.set_ylim([point[1] - 5, point[1] + 5])\n", + " ax.set_zlim([point[2] - 5, point[2] + 5])\n", + "\n", + " plt.show()\n", + "\n", + "# Define the plane parameters\n", + "point_on_plane = np.array([0, 0, 0])\n", + "vector1 = np.array([1, 2, -1])\n", + "vector2 = np.array([0, 1, 1])\n", + "\n", + "# Define the ranges for parameters u and v\n", + "# (start, end, number of steps)\n", + "u_params = (-5, 5, 50)\n", + "v_params = (-5, 5, 50)\n", + "\n", + "# Call the function to plot the plane\n", + "plot_parametric_plane(point_on_plane, vector1, vector2, u_params, v_params)\n" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
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" + }, + "metadata": {}, + "output_type": "display_data", + "jetTransient": { + "display_id": null + } + } + ], + "execution_count": 4 + }, + { + "cell_type": "markdown", + "id": "fa36f0f9-2c86-4445-8a15-258e28a37246", + "metadata": { + "id": "fa36f0f9-2c86-4445-8a15-258e28a37246" + }, + "source": [ + "Por último, queremos saber si el vector\n", + "$$ \\vec b = \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 \\end{pmatrix}$$\n", + "pertenece al $ spn\\{\\vec v_1, \\vec v_3 \\}$. Para saberlo, planteamos el sistema lineal\n", + "$$ [\\vec v_1 \\vec v_3] \\vec x = \\vec b,$$\n", + "que corresponde a la matriz aumentada\n", + "$$\\left[\\begin{array}{cc|c}1&0&1\\\\2&1&1\\\\-1&1&-3\\end{array}\\right].$$\n" + ] + }, + { + "cell_type": "code", + "id": "8f7324af-7870-479e-8223-89d499ece576", + "metadata": { + "id": "8f7324af-7870-479e-8223-89d499ece576", + "outputId": "e54a6a3a-bc65-4e64-f303-05e8359d0b23", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:09.745640012Z", + "start_time": "2026-01-31T18:43:09.549570123Z" + } + }, + "source": [ + "Al = [[1, 0, 1], [2, 1, 1], [-1, 1, -2]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 1, 0, 1],\n", + "[ 2, 1, 1],\n", + "[-1, 1, -2]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 1\\\\2 & 1 & 1\\\\-1 & 1 & -2\\end{matrix}\\right]$" + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 5 + }, + { + "cell_type": "markdown", + "id": "8d3bdb02-bfad-47e1-9745-55c18046946f", + "metadata": { + "id": "8d3bdb02-bfad-47e1-9745-55c18046946f" + }, + "source": [ + "Vamos a realizar una serie de operaciones elementales por renglón para llevar nuestra matriz a su forma escalonada. Primero, eliminamos los ceros bajo el pivote en la primer columna:" + ] + }, + { + "cell_type": "code", + "id": "e07370f6-823c-4795-92d9-4d4201abd234", + "metadata": { + "id": "e07370f6-823c-4795-92d9-4d4201abd234", + "outputId": "d99fbb64-307f-47c3-ccf8-63fb84a42689", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.053141760Z", + "start_time": "2026-01-31T18:43:09.913846210Z" + } + }, + "source": [ + "A = A.elementary_row_op(\"n->n+km\", row=1, k=-2, row2=0)\n", + "A = A.elementary_row_op(\"n->n+km\", row=2, k=1, row2=0)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 0, 1],\n", + "[0, 1, -1],\n", + "[0, 1, -1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 1\\\\0 & 1 & -1\\\\0 & 1 & -1\\end{matrix}\\right]$" + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 6 + }, + { + "cell_type": "markdown", + "id": "0e3b1eed-bb1f-42f3-8c66-d33a00570c90", + "metadata": { + "id": "0e3b1eed-bb1f-42f3-8c66-d33a00570c90" + }, + "source": [ + "Luego, eliminamos los ceros bajo el pivote en la segunda columna:" + ] + }, + { + "cell_type": "code", + "id": "7082a07a-f4c5-485a-b666-1f22e6474d58", + "metadata": { + "id": "7082a07a-f4c5-485a-b666-1f22e6474d58", + "outputId": "a6fb420e-2f03-4fb7-987c-e90466bccf80", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.157696692Z", + "start_time": "2026-01-31T18:43:10.089302515Z" + } + }, + "source": [ + "A = A.elementary_row_op(\"n->n+km\", row=2, k=-1, row2=1)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 0, 1],\n", + "[0, 1, -1],\n", + "[0, 0, 0]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 1\\\\0 & 1 & -1\\\\0 & 0 & 0\\end{matrix}\\right]$" + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 7 + }, + { + "cell_type": "markdown", + "id": "ce2ed12b-996a-431c-96f8-51157b44385e", + "metadata": { + "id": "ce2ed12b-996a-431c-96f8-51157b44385e" + }, + "source": [ + "En este punto, tenemos la respuesta: este sistema no es inconsistente y por lo tanto $\\vec b \\in {spn}\\{\\vec v_1, \\vec v_3 \\}$. Pero además nuestra matriz está en forma escalonada reducida, y por tanto tenemos la solución al sistema:\n", + "\n", + "$$\\vec v_1 - \\vec v_3 = \\begin{pmatrix} 1 \\\\ 2 \\\\ -1 \\end{pmatrix} - \\begin{pmatrix} 0 \\\\ 1 \\\\ 1 \\end{pmatrix} = \\begin{pmatrix} 1 \\\\ 1 \\\\ -2 \\end{pmatrix} = \\vec b.$$" + ] + }, + { + "cell_type": "markdown", + "id": "99e9cf6c-8e59-4c1f-9f5c-f668c4dba885", + "metadata": { + "id": "99e9cf6c-8e59-4c1f-9f5c-f668c4dba885" + }, + "source": [ + "## 2\n", + "Considere el siguiente sistema de ecuaciones lineales dependiente de un parámetro $h \\in \\mathbb{R}$:\n", + "\n", + "$$\\begin{aligned}\n", + "x_1 + hx_2 &= 2 \\\\\n", + "4x_1 + 8x_2 &= 8\n", + "\\end{aligned}$$\n", + "\n", + "1. Escriba la matriz aumentada $[A | \\vec{b}]$ y aplique operaciones elementales de fila para llevarla a su forma escalonada (REF).\n", + "2. Encuentre el valor específico de $h$ para el cual el sistema posee **infinitas soluciones**.\n", + "3. Para el valor de $h$ hallado en el inciso anterior, escriba el conjunto solución en **forma vectorial paramétrica**: $$\\vec{x} = \\vec{p} + t\\vec{v}_h$$\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "ef3ef9b9-5488-4890-a034-794db338e9b6", + "metadata": { + "id": "ef3ef9b9-5488-4890-a034-794db338e9b6" + }, + "source": [ + "En este caso, la matriz aumentada es\n", + "$$A=\\left[\\begin{array}{cc|c}1&h&2\\\\4&8&8\\end{array}\\right].$$\n" + ] + }, + { + "cell_type": "code", + "id": "dfebd2fb-66d4-4576-9097-425d64420c22", + "metadata": { + "id": "dfebd2fb-66d4-4576-9097-425d64420c22", + "outputId": "838030ba-171c-46bb-9e88-337dc39af120", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.195401554Z", + "start_time": "2026-01-31T18:43:10.161100983Z" + } + }, + "source": [ + "h = sy.symbols('h')\n", + "Al = [[1,h,2],[4,8,8]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, h, 2],\n", + "[4, 8, 8]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & h & 2\\\\4 & 8 & 8\\end{matrix}\\right]$" + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 8 + }, + { + "cell_type": "markdown", + "id": "f2300fde-a9e8-4d56-9aec-ebdf7c2f3137", + "metadata": { + "id": "f2300fde-a9e8-4d56-9aec-ebdf7c2f3137" + }, + "source": [ + "La forma escalonada de esta matriz es" + ] + }, + { + "cell_type": "code", + "id": "627658f9-7297-4a13-b087-93571fdc81a4", + "metadata": { + "id": "627658f9-7297-4a13-b087-93571fdc81a4", + "outputId": "251aab4e-b442-425c-b822-6681b9200b72", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.361825919Z", + "start_time": "2026-01-31T18:43:10.197993833Z" + } + }, + "source": [ + "A.echelon_form()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, h, 2],\n", + "[0, 8 - 4*h, 0]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & h & 2\\\\0 & 8 - 4 h & 0\\end{matrix}\\right]$" + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 9 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "De aquí podemos concluir que el sistema es inconsistente cuando\n", + "$$ 8-4h = 0 \\Rightarrow h = 2$$\n", + "y la constante en el lado derecho es distinta de cero. Pero observemos la segunda fila completa: $0x_1 + 0x_2 = 0$ cuando $h=2$.\n", + "Por el contrario, cuando\n", + "$$ 8-4h = 0 \\Rightarrow h = 2, $$\n", + "el sistema tiene soluciones infinitas, dado que tenemos un renglón de ceros y tenemos una ecuación para dos variables." + ], + "id": "ef1a82ca9510fe2e" + }, + { + "metadata": { + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.458225618Z", + "start_time": "2026-01-31T18:43:10.394971538Z" + } + }, + "cell_type": "code", + "source": "A.subs(h,2).echelon_form()", + "id": "fb4874e4a0566dbe", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2, 2],\n", + "[0, 0, 0]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2 & 2\\\\0 & 0 & 0\\end{matrix}\\right]$" + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 10 + }, + { + "metadata": {}, + "cell_type": "markdown", + "source": [ + "¿Cómo encontramos la forma paramétrica de esta solución? Sabemos que\n", + "\n", + "$$x_1 + 2 x_2 = 2 \\Rightarrow x_2 = 1 - \\frac{x_1}{2}.$$\n", + "Luego, en términos de un parámetro $t$, la solución tiene la forma \n", + "$$ \\vec x = \\begin{pmatrix}t \\\\ 1 - \\frac{t}{2} \\end{pmatrix} = \\begin{pmatrix}0\\\\ 1 \\end{pmatrix} + t \\begin{pmatrix}1 \\\\ -1/2 \\end{pmatrix}.$$\n", + "El primer vector corresponde a la *solución particular*, es decir, $x_1=0, x_2 = 1$ resuelven el problema original con $h=2$, mientras que el segundo vector representa una *solución homogénea*: si $x_1$ es cualquier valor $t$, y $x_2 = 1- t/2$, tenemos una solución al sistema original con $\\vec b = 0$.\n", + "\n" + ], + "id": "e1dccbcc50bcca06" + }, + { + "cell_type": "markdown", + "id": "9a6b5985-b380-421b-8c20-f5c5cf2bed5a", + "metadata": { + "id": "9a6b5985-b380-421b-8c20-f5c5cf2bed5a" + }, + "source": [ + "## 3\n", + "Sea la matriz $A$ y el vector de pesos $\\vec{x}$:\n", + "\n", + "$$A = \\begin{pmatrix} 1 & 5 & -2 \\\\ -3 & 0 & 1 \\end{pmatrix}, \\quad \\vec{x} = \\begin{pmatrix} 2 \\\\ 1 \\\\ 4 \\end{pmatrix}$$\n", + "\n", + "1. Calcule el producto $A\\vec{x}$ utilizando **exclusivamente** la definición de combinación lineal de las columnas de $A$:\n", + " $$x_1\\vec{a}_1 + x_2\\vec{a}_2 + x_3\\vec{a}_3 = \\vec{b}$$\n", + "2. Si se sabe que la ecuación $A\\vec{x} = \\vec{0}$ admite una solución no trivial $\\vec{x} = \\begin{pmatrix} 1 \\\\ 1 \\\\ 2 \\end{pmatrix}$, ¿qué podemos afirmar sobre las columnas de $A$?" + ] + }, + { + "cell_type": "code", + "id": "ce28cb87-dcde-4b5b-bba0-2fc6e632e679", + "metadata": { + "id": "ce28cb87-dcde-4b5b-bba0-2fc6e632e679", + "outputId": "d57bbe0a-62d0-433a-86e0-771ee999ecde", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.551258903Z", + "start_time": "2026-01-31T18:43:10.462669308Z" + } + }, + "source": [ + "Al = [[1,5,-2],[-3,0,1]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 1, 5, -2],\n", + "[-3, 0, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 5 & -2\\\\-3 & 0 & 1\\end{matrix}\\right]$" + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 11 + }, + { + "cell_type": "code", + "id": "8482c529-15cd-47ad-9d97-96c8e6a8a03a", + "metadata": { + "id": "8482c529-15cd-47ad-9d97-96c8e6a8a03a", + "outputId": "c9220c19-04e4-4b98-ed22-6a36894d59a7", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 78 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.596586744Z", + "start_time": "2026-01-31T18:43:10.562581863Z" + } + }, + "source": [ + "xl = [2,1,4]\n", + "x = sy.Matrix(xl)\n", + "x\n" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[2],\n", + "[1],\n", + "[4]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}2\\\\1\\\\4\\end{matrix}\\right]$" + }, + "execution_count": 12, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 12 + }, + { + "cell_type": "markdown", + "id": "a8b64d5f-f869-495a-be01-eb10482078b8", + "metadata": { + "id": "a8b64d5f-f869-495a-be01-eb10482078b8" + }, + "source": [ + "Vamos a calcular la combinación lineal:" + ] + }, + { + "cell_type": "code", + "id": "bdafd480-49e8-43a1-8b9f-f7cd863cd39f", + "metadata": { + "id": "bdafd480-49e8-43a1-8b9f-f7cd863cd39f", + "outputId": "15a6923b-9551-459f-bed5-5c7a66055b56", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.641194892Z", + "start_time": "2026-01-31T18:43:10.604208176Z" + } + }, + "source": [ + "x[0]*A[:,0] + x[1]*A[:,1] + x[2]*A[:,2]" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[-1],\n", + "[-2]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1\\\\-2\\end{matrix}\\right]$" + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 13 + }, + { + "cell_type": "code", + "id": "f20304f9-8806-4863-96bd-c89b20d60c42", + "metadata": { + "id": "f20304f9-8806-4863-96bd-c89b20d60c42", + "outputId": "95176e65-de1b-41c2-c858-b12e56629a0d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.679145718Z", + "start_time": "2026-01-31T18:43:10.647324937Z" + } + }, + "source": [ + "A*x" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[-1],\n", + "[-2]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}-1\\\\-2\\end{matrix}\\right]$" + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 14 + }, + { + "cell_type": "markdown", + "id": "e2166405-28cc-4697-ab33-bb864fd54e88", + "metadata": { + "id": "e2166405-28cc-4697-ab33-bb864fd54e88" + }, + "source": [ + "Se nos da una solución al problema $A\\vec x = 0$:\n", + "$$\\vec x = \\begin{pmatrix} 1\\\\ 1 \\\\ 2\\end{pmatrix}.$$\n", + "Esto significa que, si denotamos las columnas de A como $\\vec a_1, \\vec a_2, \\vec a_3$, la combinación\n", + "$$\\vec a_1 + \\vec a_2 + 2 \\vec a_3 = 0 $$" + ] + }, + { + "cell_type": "code", + "id": "ad3600aa-abd6-4022-bf98-08e3608a243c", + "metadata": { + "id": "ad3600aa-abd6-4022-bf98-08e3608a243c", + "outputId": "55faf3e6-8bc9-43e5-d927-9eacbe07d12d", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.723848286Z", + "start_time": "2026-01-31T18:43:10.682499513Z" + } + }, + "source": "A[:,0] + A[:,1] + 2*A[:,2]", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[ 2],\n", + "[-1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}2\\\\-1\\end{matrix}\\right]$" + }, + "execution_count": 15, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 15 + }, + { + "cell_type": "markdown", + "id": "b1a8e840-fed8-4df2-b9f2-3237d4d86291", + "metadata": { + "id": "b1a8e840-fed8-4df2-b9f2-3237d4d86291" + }, + "source": [ + "\n", + "Por lo tanto, uno de estos vectores puede reescribirse en términos de los otros. Por ejemplo:\n", + "$$ \\vec a_2 = -\\vec a_1 - 2\\vec a_3$$\n" + ] + }, + { + "cell_type": "code", + "id": "248282cb-699e-41b5-a248-7cdd21534024", + "metadata": { + "id": "248282cb-699e-41b5-a248-7cdd21534024", + "outputId": "79c3bf72-f0e0-44be-d50f-0d47df4581d1", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.773915764Z", + "start_time": "2026-01-31T18:43:10.738755729Z" + } + }, + "source": "A[:,1] == -A[:,0] - 2*A[:,2]", + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 16 + }, + { + "cell_type": "markdown", + "id": "c90d490f-efb6-4f6e-84a6-d07519b23c33", + "metadata": { + "id": "c90d490f-efb6-4f6e-84a6-d07519b23c33" + }, + "source": [ + "Luego entonces,\n", + "\n", + "$$\\text{span}\\{\\vec a_1,\\vec a_2,\\vec a_3\\}=\\text{span}\\{\\vec a_1,\\vec a_3\\}.$$\n" + ] + }, + { + "cell_type": "markdown", + "id": "1f796754-7393-4376-b875-c41165b7d5b4", + "metadata": { + "id": "1f796754-7393-4376-b875-c41165b7d5b4" + }, + "source": [ + "## 4\n", + "Dadas las siguientes matrices de \"cizallamiento\":\n", + "\n", + "$$A = \\begin{pmatrix} 1 & 2 \\\\ 0 & 1 \\end{pmatrix}, \\quad B = \\begin{pmatrix} 1 & 0 \\\\ 2 & 1 \\end{pmatrix}$$\n", + "\n", + "1. Calcule los productos $AB$ y $BA$. Demuestre explícitamente que $AB \\neq BA$.\n", + "2. Si $A$ representa una deformación horizontal y $B$ una deformación vertical, ¿por qué el estado final del sistema depende del orden en que se aplican estas deformaciones?\n", + "3. Calcule $(AB)^T$ y verifique numéricamente la identidad fundamental:\n", + " $$(AB)^T = B^T A^T$$" + ] + }, + { + "cell_type": "markdown", + "id": "1dd12102-54c6-4a9e-bc58-5094a06be49d", + "metadata": { + "id": "1dd12102-54c6-4a9e-bc58-5094a06be49d" + }, + "source": [ + "Definimos nuestras matrices:" + ] + }, + { + "cell_type": "code", + "id": "c5e06ea9-146e-4335-82df-ad2f9db5ea76", + "metadata": { + "id": "c5e06ea9-146e-4335-82df-ad2f9db5ea76", + "outputId": "70eca042-0241-4c08-e1fd-b4113991a08c", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.843697057Z", + "start_time": "2026-01-31T18:43:10.796542885Z" + } + }, + "source": [ + "Al = [[1,2],[0,1]]\n", + "A = sy.Matrix(Al)\n", + "A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2],\n", + "[0, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\0 & 1\\end{matrix}\\right]$" + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 17 + }, + { + "cell_type": "code", + "id": "14e27cb3-47e9-4448-87ac-05248c548698", + "metadata": { + "id": "14e27cb3-47e9-4448-87ac-05248c548698", + "outputId": "32c819f5-88cc-4383-fda3-8f27fc2d28e2", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.878178417Z", + "start_time": "2026-01-31T18:43:10.846024746Z" + } + }, + "source": [ + "Bl = [[1,0],[2,1]]\n", + "B = sy.Matrix(Bl)\n", + "B" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 0],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 0\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 18 + }, + { + "cell_type": "markdown", + "id": "5f5cb42a-7ca7-4205-8658-1c3a88336952", + "metadata": { + "id": "5f5cb42a-7ca7-4205-8658-1c3a88336952" + }, + "source": [ + "Evaluamos los productos:" + ] + }, + { + "cell_type": "code", + "id": "2dff8d1b-68b8-4727-ab55-5731b0e08ce3", + "metadata": { + "id": "2dff8d1b-68b8-4727-ab55-5731b0e08ce3", + "outputId": "c4534ee7-b84c-4e0e-e726-ace07489e41e", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.929300959Z", + "start_time": "2026-01-31T18:43:10.894990384Z" + } + }, + "source": [ + "A*B" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[5, 2],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}5 & 2\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 19 + }, + { + "cell_type": "code", + "id": "c7646525-8450-475c-b042-0956b0e5761f", + "metadata": { + "id": "c7646525-8450-475c-b042-0956b0e5761f", + "outputId": "508f1417-90b9-45f0-a9fa-fbee297c6994", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:10.967053376Z", + "start_time": "2026-01-31T18:43:10.931822104Z" + } + }, + "source": [ + "B*A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2],\n", + "[2, 5]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\2 & 5\\end{matrix}\\right]$" + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 20 + }, + { + "cell_type": "markdown", + "id": "9d2a201d-6a1c-42a1-b8c5-573a36298292", + "metadata": { + "id": "9d2a201d-6a1c-42a1-b8c5-573a36298292" + }, + "source": [ + "Claramente, $AB\\neq BA$:" + ] + }, + { + "cell_type": "code", + "id": "31cfb6dc-1849-42e3-8cc3-af75e0e1ac87", + "metadata": { + "id": "31cfb6dc-1849-42e3-8cc3-af75e0e1ac87", + "outputId": "435d2352-a7ab-4cb2-8178-a5996c290929", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.041116648Z", + "start_time": "2026-01-31T18:43:10.981263839Z" + } + }, + "source": [ + "A*B == B*A" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "False" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 21 + }, + { + "cell_type": "markdown", + "id": "74675073-b17c-4f99-8196-496fe0c8dbdc", + "metadata": { + "id": "74675073-b17c-4f99-8196-496fe0c8dbdc" + }, + "source": [ + "Para clarificar el efecto de estas matrices, consideremos el triángulo con vértices en los puntos $(-1,0), (1,0)$, y $(0,2)$. Vamos a ver el efecto de aplicar AB y BA a estos puntos:" + ] + }, + { + "cell_type": "code", + "id": "1516a3a0-4d64-4493-aad8-a3240ad67dd0", + "metadata": { + "id": "1516a3a0-4d64-4493-aad8-a3240ad67dd0", + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.116280767Z", + "start_time": "2026-01-31T18:43:11.075949739Z" + } + }, + "source": [ + "vert = [[-1, 0], [0,2], [1, 0]]\n", + "ABvert=[(A*B*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "BAvert=[(B*A*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "ABvertices = np.array(ABvert)\n", + "BAvertices = np.array(BAvert)\n" + ], + "outputs": [], + "execution_count": 22 + }, + { + "cell_type": "markdown", + "id": "ea868e22-9bdb-4e9b-9a87-1d94c0e4b68a", + "metadata": { + "id": "ea868e22-9bdb-4e9b-9a87-1d94c0e4b68a" + }, + "source": [ + "Al aplicar AB, terminamos con un triángulo con vértices en los puntos $(-5,-2), (4,2)$ y $(5,2)$." + ] + }, + { + "cell_type": "code", + "id": "9d930e3a-40c9-4277-a77a-b9b46a8f5a29", + "metadata": { + "id": "9d930e3a-40c9-4277-a77a-b9b46a8f5a29", + "outputId": "2a72c25f-702d-4be9-82a0-2fd3306e3d70", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.184756752Z", + "start_time": "2026-01-31T18:43:11.119226145Z" + } + }, + "source": [ + "ABvert" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "[[-5, -2], [4, 2], [5, 2]]" + ] + }, + "execution_count": 23, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 23 + }, + { + "cell_type": "markdown", + "id": "7f37c8a0-909f-4e6b-8299-03b832673bc8", + "metadata": { + "id": "7f37c8a0-909f-4e6b-8299-03b832673bc8" + }, + "source": "Al aplicar BA, terminamos con un triángulo con vértices en los puntos $(-1,-2), (4,6)$ y $(1,2)$. ¡Estos son triángulos muy diferentes!" + }, + { + "cell_type": "code", + "id": "4b7a8ea1-2bc5-4ae2-8e9a-ce2face0c759", + "metadata": { + "id": "4b7a8ea1-2bc5-4ae2-8e9a-ce2face0c759", + "outputId": "91b61957-54f3-40df-e250-bc40537a6c90", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.228580539Z", + "start_time": "2026-01-31T18:43:11.197151857Z" + } + }, + "source": [ + "BAvert" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "[[-1, -2], [4, 10], [1, 2]]" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 24 + }, + { + "cell_type": "markdown", + "id": "67c4c8a9-22b2-41a6-81ca-729d124a73d1", + "metadata": { + "id": "67c4c8a9-22b2-41a6-81ca-729d124a73d1" + }, + "source": [ + "Vamos a visualizarlos. En azul está en triángulo original, en rojo el triángulo al que aplicamos AB, y en verde al que aplicamos BA." + ] + }, + { + "cell_type": "code", + "id": "d9e5e256-1412-4d3d-ad2f-89326b29e788", + "metadata": { + "id": "d9e5e256-1412-4d3d-ad2f-89326b29e788", + "outputId": "03f2016a-0fb0-4a6e-f7c2-d0470d719d31", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.348724945Z", + "start_time": "2026-01-31T18:43:11.234649509Z" + } + }, + "source": [ + "from matplotlib.patches import Polygon\n", + "from matplotlib.path import Path\n", + "from matplotlib.patches import PathPatch\n", + "\n", + "# Define the vertices of the triangle (x, y coordinates)\n", + "# Example: an arbitrary triangle with 3 points\n", + "vertices = np.array(vert)\n", + "\n", + "# Create a figure and an axes\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Create a Polygon patch\n", + "# facecolor='blue' fills the triangle, edgecolor='black' adds an outline\n", + "triangle = Polygon(vertices, closed=True, facecolor='blue', edgecolor='black')\n", + "ABtriangle = Polygon(ABvertices, closed=True, facecolor='red', edgecolor='black')\n", + "BAtriangle = Polygon(BAvertices, closed=True, facecolor='green', edgecolor='black')\n", + "\n", + "# Add the patch to the axes\n", + "ax.add_patch(triangle)\n", + "ax.add_patch(ABtriangle)\n", + "ax.add_patch(BAtriangle)\n", + "\n", + "# Set the axis limits for better viewing\n", + "ax.set_xlim(-5.5, 5.5)\n", + "ax.set_ylim(-2.5, 10.5)\n", + "ax.set_aspect('equal', adjustable='box') # Ensures the triangle isn't stretched\n", + "\n", + "# Add labels and a title\n", + "#plt.xlabel('X-axis')\n", + "#plt.ylabel('Y-axis')\n", + "#plt.title('Triangle drawn with Matplotlib')\n", + "#plt.grid(True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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" + }, + "metadata": {}, + "output_type": "display_data", + "jetTransient": { + "display_id": null + } + } + ], + "execution_count": 25 + }, + { + "cell_type": "markdown", + "id": "f854f28a-826c-4dc0-a080-a203664a76f6", + "metadata": { + "id": "f854f28a-826c-4dc0-a080-a203664a76f6" + }, + "source": [ + "Podemos visualizarlo mejor si utilizamos una deformación más pequeña." + ] + }, + { + "cell_type": "code", + "id": "660e17c9-88c9-435e-b606-9b25044f304b", + "metadata": { + "id": "660e17c9-88c9-435e-b606-9b25044f304b", + "outputId": "26e068aa-9bc5-4d0d-dc27-b87e9c8ef675", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 430 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.568243361Z", + "start_time": "2026-01-31T18:43:11.374055939Z" + } + }, + "source": [ + "Al2 = [[1,1.1],[0,1]]\n", + "A2 = sy.Matrix(Al2)\n", + "Bl2 = [[1,0],[1.1,1]]\n", + "B2 = sy.Matrix(Bl2)\n", + "vert = [[-1, 0], [0,2], [1, 0]]\n", + "ABvert2=[(A2*B2*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "BAvert2=[(B2*A2*sy.Matrix(x)).T.tolist()[0] for x in vert]\n", + "ABvertices2 = np.array(ABvert2)\n", + "BAvertices2 = np.array(BAvert2)\n", + "\n", + "\n", + "# Define the vertices of the triangle (x, y coordinates)\n", + "# Example: an arbitrary triangle with 3 points\n", + "vertices = np.array(vert)\n", + "\n", + "# Create a figure and an axes\n", + "fig, ax = plt.subplots()\n", + "\n", + "# Create a Polygon patch\n", + "# facecolor='blue' fills the triangle, edgecolor='black' adds an outline\n", + "triangle = Polygon(vertices, closed=True, facecolor='blue', edgecolor='black')\n", + "ABtriangle2 = Polygon(ABvertices2, closed=True, facecolor='red', edgecolor='black')\n", + "BAtriangle2 = Polygon(BAvertices2, closed=True, facecolor='green', edgecolor='black')\n", + "\n", + "# Add the patch to the axes\n", + "ax.add_patch(triangle)\n", + "ax.add_patch(ABtriangle2)\n", + "ax.add_patch(BAtriangle2)\n", + "\n", + "# Set the axis limits for better viewing\n", + "ax.set_xlim(-2.5, 2.5)\n", + "ax.set_ylim(-2.5, 5.5)\n", + "ax.set_aspect('equal', adjustable='box') # Ensures the triangle isn't stretched\n", + "\n", + "# Add labels and a title\n", + "#plt.xlabel('X-axis')\n", + "#plt.ylabel('Y-axis')\n", + "#plt.title('Triangle drawn with Matplotlib')\n", + "#plt.grid(True)\n", + "\n", + "# Display the plot\n", + "plt.show()" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "
" + ], + "image/png": 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pYv1VMZ6AqhkHqDU9oLatDqeK+ZTpaz4zx/cpZKRIZVPFeAKoZlzzZK/tQTqtwNuWz5GiwvyEFwO/zvO5QoWMFKlsqhiP5WomZtZOOtLO4fcQ4LMx3hxba4BLCrhCU8hIEcqlivFYrGaSwFkB9JMkgxlGEDfbfwArgI8WeDzdXZIilEsV47FUzTjA8Wawjm2v23+20CvKnga+5tOTtKpkpMjkU8V4LFQzVWbGuyA0273iw0T3CyY3/aKQkSKTTxXjsVDNnBbQHfLdZtShhUuluLnr/iBwm4UZQhUyUkQKqWI8PlUzjsm74wo/VFZesjfz01Rza/pTdg6vkJFiUkgV4/GpmrE5pWYmPg8jiAPVwO3A7814TlsUMlIk/KhiPAVWMzFgDHCYD03Jxg5gg38P4DnAx0wXz6wAborp7pIUCT+qGI8P1cxUn5qSjTX+BEzcBMrXgGdMTgZBlYwUAT+rGE+e1YwDnAQc4GNTBrK68EPEgXrgCfP8i+0Hk9PPbZtCRgrkZxXjybOa+RAwyeem9KfNrEiQJ+9S6HOmIPqEX+3KgUJGIs5GFePJo5o50/SYBuWF/DtN4mbM5v3AEvPnMChkJOJsVDGeHKoZx1xvfMxSUzJxCxtx3WAerTnP73blSCEjEWazivFkWc14t6yD/Ne8yUxQlQNvtcZbgT8BUVi6UHeXJMJsVjGeLKoZx0wBd4jlpqTLcRiBY+4YPW+iMyofPFUyElFBVDGeAaqZIKbUTNdlemqzGEbgrdb4f03AjA2ifTlQyEhEBVHFeAaoZhqAREBN8bxilj0ZQBw4CHjMrBoQZJ90thQyEkFBVjGeDNWMY0YOBjGlZrrm/u8qed86D/h7gAPB86E+GYmgIKsYT4ZqxjWTUVldnjCD94GX+76rFDdxeA/wM+DDATcvV04AIaCQkRyEUcV4UqqZGDAywGfvUw0wpcNEs8vFQbapQKUwPkpKRhhVjMerZpz/qWLCWEAtw4hrb7XGm4DHzex1xUSVjEREmFWM5yJw3J6p4Q4K4fRbgc17XirFzDy7q4CvBji7hJ9st1khI1kKs4rxfAuqnfB6UlOGEXgfnDmmH/jYkJrkB9shEHS3mRSlKFQxf+kZ5XN6SM1IGUYQNx26d5vlnIqdLpckAsKuYlxw5sDgeM9iQ2F401wuAWebKTFLIWAI4HJJlYwMIApVzL3g/iX48UmpzDCCRUn415D6nG3R5ZKELOwq5j2IfQUOd2BkCItMA3T39Mf8axJmhtMCq3S5JCGKQhXzrZ7ZoaaGFDCYOXw/gMvDa4FVurskIQq7inkVnG/DycnwHp11gWfhiFjPYO9Ss8Y8xGyT1ZCZNGkSDz74IC0tLbiuy/Tp022eTnwVhSrmK7CvCyeH2IRlPcMIrk+WVj/MGuB84JhiD5mamhqam5uZM2eOzdOIFWFXMX8GfgNTu3qWmw3DM8B/wbd7HgMsCX8D/sWEy2/Ma12Wz2m14/fhhx/m4YcftnkKsSLsKqar55Z1fQyOsbD2azbWAH+Eq8xghmL3AjAfeCDlQ287XDzqk5EMwq5ifgTui3B2SNcoG8D5dc8gx+8U+e3q1cD/MpMH/s68FlS4eCJ1C7uqqorq6v+Z2ieRCHo2Igm/itkCznU9n4r6EE7fAvH74HS3ZxWBYv0tvBq4HngwhMolXaR+hvPmzaO9vb13a2lpCbtJZSjsKub/QcV7wU+pCfAuxO+GY7vh126wi6z55a/Ap81Yqj+Y18IKF0+kQqaxsZHa2trebdiwKMznXk7CrmLWALfBKd2wX8Cn7oCKO2FkJzzsQk3Apy/U88CngPE9XUkQgXDxROpyqbOzk87OzrCbUcbCrGJccK6AOgc+HvCp34f4XTDoPXgs2fNTKBbPmcuihyJwWdQXqyFTU1PDqFGjer8eOXIk48aNY8uWLWzatMnmqSVnYVcxvwV3ec/4pCB/9e2G2L1Q0waPuXBogKcuxLMmXP4Q4XDxOPmvgTewhoYGli9fvtfrS5Ys4dJLLx3w/YlEgvb2dmpra+no6LDUSukxCHgjpJD5AGJj4COb4fMB3lFKgvNzqHoZlrnhzEmeq1UmXB424RJWsOTy2bT6O+Pxxx/HcYr5BmC5CLuK+S64m+AsN7iAcYHfg/MS/CqkRQ9y8YwJl0eKoHJJF6mOXwlLmH0xb4LzDfi4C4MDPO2ynt7Sn5j5YaJqJTDVTFD+mHmtWMLFo5Ape2FXMV+F6t09i7QFJWW4wIwAT5uLp4EppsL6s3mt2MLFo5Ape2FWMSt7Viia0h1cxkV8uMBTJlxOArzezGINF49CpqyFWcUke8YnHRQPbhbuCA8XeJKe6Ys/Ya7kKIFw8UTqORkJWphVzN3gPt/TIRLEr7qIDhdYAfy7qVq8yaO6Q26T36Lys5bAhVnFdEBsLhztBLMSWgSHCzwBnAJMMkFDCYaLRyFTtsKsYr4JzhaYEsCUmh0Qj9Bwgcfp6eOenBIupXJZ1BeFTFkKs4pZD84CmJTsWXnWJjNcYHAEhgssN8Fyiul/oYQrl3QKmbIUZhVzFdS4PbdPbEodLpAMb7jAcnNJdKq5c0QZhYtHIVN2wqxiHu15zHZat90pNZPg/BIqN/dcIh1l8VSZuObZlpNNuDxtXi+3cPEoZMpOWFXMbohdAcNjcLTF06QOFwh4PJJrnso92dyOXmleL9dw8ShkykqYVcxtkHwZPml5AGQIwwVcYKl5xuUM80AxCpdeCpmyElYV0wbO13vWsR5q8TQBDxdwgT+ZR/+nmBHSKFz2opApG2FWMV+Hyp1wmsVTBDhcwDW9SxOBM83cLihc+qSQKRthVTHNPasPnNpt7yGVgIYLuGaqhY+bkdHPmdcVLv1TyJSFsKoYM6XmATE4wdIpzHCBKRaHC7hm3twTgGlmPl0ULlnT2KWyEFYV8ytwn4CzLK3qbnm4gBcu/26CpVTHFtmmSqbkhVXFvA+xK2G0A6MtHN7icAHXTMx9nLlD1WxeV7jkRyFT8sKqYr7TM+vdNAvjkywNFzCP2DAeOEfh4huFTEkLq4rZBM7/h4mu/wOGLAwXcM0SrseatYv+Zl5XuPhDIVPSwqpivgr7dPWMCPSTz8MFXLOM6z+ZVRcVLnYoZEpWWFXMk8DPeqbU3MfHw/o4XMAFfgOMI85084gNPRkmFihkSlYYVUwSnFlwsNNTHvjJh+ECSeAB4GPEORf4OycBM0jqY2CVfrolKawq5hpw18InXX//ZRU4XCAJ/NqEyz8Df+cTwHK6+S/gVmBfHxsr6RQyJSnoKmYXcAU434Fj8HfylgKGCyR7ntThGOL8C7COScB/keydnw56Zs6aq4+CRfrJlpygq5g1xBmPww9w4mYYsl/yHC6QBH4JHE2c84AXmQw8QZJlZgqpdF9WNWORQqbkBFXFJIFbiTGeQ3mRGOBOAup8OnwewwWSwP0mXM4HXqYBWEGydwqpvqiasUk/1ZISVBXTQowzgKv4P+xmtJPEqcW/KTVzHC7QDfwcOIo4FwAvm5l0kzxmZnnJhqoZWxQyJSWIKuaXxDmKQTzBo2aqg0dd6JqGP4OHchgu0N1zs5yjqOAi4BUzk26SpXkknqoZW/QTLRm2q5h24BLgfD5NB3+niwbgihjERgBH+nCKLIcLdAP3AUdSwWeA9WYm3WTvFFL5UjVjg0KmZNisYp6kgrF8iLtZAvwKlwOBJmBjEpJn+TCJSxbDBbqBe4EjiHMxsMHMpJvsnUKqUKpmbNBPsyTYqmJ2A1/HYRITaGENSWaYs70N/LsD7nHAwQWeZoDhAt3APcAYKvgssJEzgWdI8rCZQspPqmb8ppApCTaqmJeIcwJxbuQ/cFlBko+mfPdrwAdVFD6lZj/DBbqAnwKHU8HngFc5E1hFkj9gbxYsVTN+00+y6PldxbjA7cQYxwj+xtO4fC1tdrPngR8D3af58Es/w3CBLuAu4HDifB54janAX0jyEHB8gSfMhqoZPylkip6fVUwrMc4GvsQX2cULdO/1kXaByx2IHWhmdSpE2nCBLuBOYDQVzABe4yzgWZL83oeT5ULVjJ/0UyxqflYxvyPOkdTxKL/rWSUp4+3jXwBPu9D9yQKn1EwZLnAlPQ/cjaKCS4DXOQt4Dpff0bOOShhUzfglkJC57LLLePXVV3n//fdZuXIlxx8fRMlbDvyoYnYAs4BPM5VtrKObc/rYcydwVQycw4HDCjilGS7wGXoWkxxFBZcCb3A28FdcHjTz04VJ1YxfrP8EL7jgAhYsWMANN9zA+PHjaW5u5pFHHmHw4MG2T13i/Khi/kKcY9iHO7gd+D0uQ/rZ+9tAK+BOK+CUZrjAUS48QZyZwCbOAVbj8hv8nyOiEKpm/GA9ZL7yla+waNEilixZwrp165g9ezY7d+7kC1/4gu1Tl7hCqpgu4Js4nMg43qCZJLMGeNTldaDRgeRJwAF5nvZdiN0NsW5Y60ILnwaacXkAGJfnQW1SNeMHq0uiVFZWMmHCBBobG3tfc12XpUuXcuKJez+ZWVVVRXV1de/XiUTCZvOKWBzYDtTn8d5u4uwkSTdfN8t9ZDMaYC6Q/FAfg5iz0dHTq5vshKQbB/bFZZm5vRRlXZozr0BWQ2bQoEFUVFTQ2tq6x+utra0cccQRe+0/b9485s+fb7NJJaLbbNtyfmfcRNPPchjd87iZOoEzgeqB99/L++ae9Hve57XbpI6Ug0jVgY2NjdTW1vZuw4YNC7tJJcO7FPq8ubGTbcB0A3MciA8FPpbHiXebsQBtKgjKldVKpq2tja6uLoYM2bM7cciQIbz11lt77d/Z2UlnZ6fNJpWlCnM7+g7gvBzf+2N6+k84O49fSd7sUZvNAzZSlqxWMrt37+a5557j9NNP733NcRxOP/10nn76aZunlhQNwN/zCJitwDWO6ZM9JMc3eyulvaSAKXfW18JesGABd955J88++yyrVq3iyiuvpKamhsWLF9s+dVmLm98g3wEuz/O3yQ1AR75Tai5LWZleypr1kPnFL37B4MGD+cY3vsHBBx/M6tWrmTZtGm+//bbtU5ctBzjCzBZ3dJ7HWAf8AOhuAHK9yWeGC4hg/j1GtphNJBK0t7dTW1tLR4fuRgwkZv5nzgX+I88bQZhjTHHg8VroujzHGe/WeLeipJTl8tm0XslIMOLAYHMj59QCj/UQ8JgLnJVjwGwwCxyJpIjULWzJnXdr+nzTuVtowOzyptQcCYzJ4Y0tZk7MyNbFEhZVMkWsgp7lpn9Iz9pEfvg+8LoLbi5Tar4L3G0eqlHISBqFTBGbaGaOG+HT8TYCX3PAPR44KMs3meECdCpgJDNdLhWZuPnNcBOw3KeA2QksMAsO7K4GTsnyjXsNFxDZmyqZIhIDPmpuTR/rw/F2mMmpGoEt3ounZzm7QepwAVUw0g+FTBGImUJhjqlgCp0HbwfwnyZctnkZ4ZjZI7KZK0rDBSQHCpmIiwMfNn0vUws81nsmXL6VGi4eb3zSQFNqpg4XEMmCQibizjEDGwcVcIz3zEJs3zKz0OxVfMSAw4GRWRxMwwUkRwqZCKowz8A1mYVh812cscMc46a+wiVVNmWShgtIHhQyEeOYbpF7C5iru8OMO7rJ/LnfGz8OcLK5JuuPWV1AJFcKmYiIm0pjPjAvz/8x7cBC4OZswsWzrwmZ/mi4gBRAIRMBMWC4mRIzn5Wd282Tujfn88jKVKCqn+9ruIAUSCETIm8I/EzgFmC/HN+/3YTLd/IJF8dM9ntMP/touID4QCETkgozTcsS4NM5vndbSrjsyPdhWxf4ZD+9yhouID5RyITkDGAxcHAO79kGfM+Ey85CnuT3ptTsa552DRcQHylkAlRhOni/C8zO4db0NuBWc0lVULikNuT0Pr6n4QLiM4VMQBwzFebPzNSY2dhqAmmBKS58KypO6WNKTQ0XEAsUMpbFzWd3HnD9ADdyPFtMuHzX73BxgLo+bmFpuIBYopCxKA4MNXeAB3oUBRMuC0y4fGCjO8SbUjPT/3UNFxBLFDIWeLemLzYPx9UNsP+7JlxutRUumIdxPmLGKKXTcAGxSCHjswrzEO0i4IIB9m1LCZdO8ziKNV4Vk97brOECYplCxmcnm+fX+ltwsc3cKfLCxfpdYsf0wwxOe13DBSQAChkfxM3n+NvAl/uZ0/Qd84zL982dYquVS6pqs1ZtKg0XkIAoZArkTcXy836e0H/bhMvCoMPFMyVtOj0NF5AAKWTy5E2JeRXwTbM0Sbq3zaDFH4QVLo65REqdEFjDBSRgCpk8xM1Mdff08eBsqwmXprDCxeNNqeldv2m4gIRAIZMD79b0PwO3Awekff+tlHDpCjNcMMFyZMqaKRouICFRyGSpwvSf3g58Nu1O8Fum07fJBEuo4eJxTF8MGi4g4VLIZOkEc3n0kZTX/mGmuLwtSuGCCZhJwP4aLiDhU8j0w1sd5JvA1Slfv2nC5faohYunBjjJ/FnDBSRkCpk+xMwKIT9PWe+sJSVcklEMF880MxJTwwUkArQWdhrvB/IloNkETAtwhQmd/wz7jlF/vMmCj9ZwAYkOVTIp4qYb4y4zM+Vm4KvAD03XRiSDJVXSNHyjhgtIdChkUnwS+LEZCT0H+FGxhAspCzYlNVxAosXa5dJ1113Hk08+yY4dO9i6daut0xSswjytu8g8mXs98FFTvYT+rEsuKs28vRouIBFjLWSqqqq4//77ue2222ydomAO8E/AQ8CzZsXGHxVbuHiOM8/CaLiARIy1y6X58+cDMGPGDFunyJu3WuP/Nik7tZgui9I5ZgKblzRcQKIpUn0yVVVVVFdX936dSGSa7bowMfO5PAr4aTGHi8c1SxjsVAUj0RSpW9jz5s2jvb29d2tpafHt2N4wgKS5HFpXrJdFqVL/7ylgJKJyCpnGxkZc1+13GzNmTN6NaWxspLa2tncbNqyv1cdyU5HyGfRKty5fjhwy79JIASMRltPl0i233MKSJUv63Wfjxo15N6azs5POzs6839+XLvMX7SqVcCFlSLhIxOUUMm1tbbS1tdlrjY/i5lKo5MLFo4CRImGt43f48OEccMABHHroocTjccaNGwfA+vXr2bFjh63TQtov+ZILF1Km5RMpEq6NbfHixW4mDQ0NWR8jkUi4ruu6iUTCShu1adOW35bLZzPSV/aJRIL29nZqa2vp6OgIuzkiYuTy2YzULWwRKT0KGRGxSiEjIlYpZETEKoWMiFilkBERqxQyImKVQkZErFLIiIhVChkRsUohIyJWKWRExCqFjIhYpZAREasUMiJilUJGRKxSyIiIVQoZEbFKISMiVilkRMQqhYyIWKWQERGrFDIiYpVCRkSsUsiIiFUKGRGxSiEjIlYpZETEKoWMiFilkBERqxQyImKVQkZErFLIiIhVChkRsUohIyJWWQuZESNGcMcdd7Bx40Z27tzJ+vXrmT9/PpWVlbZOKSIRVGHrwEcccQSxWIxZs2axfv16xo4dy6JFi6ipqeHqq6+2dVoRiSA3qG3u3Lnuhg0bst4/kUi4ruu6iUQisDZq06Zt4C2Xz6a1SiaTuro6tmzZ0uf3q6qqqK6u7v06kUgE1DIRsSmQ5DvssMPcbdu2uTNnzuxzn+uvv97NRJWMNm3R2nK8ysjt4I2NjRmDINWYMWP2eE99fb37yiuvuIsWLer32FVVVW4ikejd6uvrFTLatEVwyyVkHPOHrA0aNIgDDzyw3302btzI7t27ARg6dCjLly9n5cqVXHLJJbhu9qdLJBK0t7dTW1tLR0dHLs0UEYty+Wzm3CfT1tZGW1tbVvvW19ezbNkynnvuOS699NKcAkZESoO1jt/6+nqWL1/O66+/zty5cxk8eHDv91pbW22dVkQixlrITJkyhdGjRzN69GhaWlr2+J7jOLZOKyIRY+2J3zvvvBPHcTJuIlI+NHZJRKxSyIiIVQoZEbFKISMiVilkRMQqhYyIWKWQERGrFDIiYpVCRkSsUsiIiFUKGRGxSiEjIlYpZETEKoWMiFilkBERqwJdEiVfWhpFJFpy+UxGOmS8v0j6zHoiEg2JRGLAicRzXq0gaPX19VZWKkgkErS0tDBs2LCiWwmhWNuudgfLdrsTiQRvvvnmgPtFupIBsvpLFKKjo6Oo/uGkKta2q93BstXubI+pjl8RsUohIyJWlW3I7Nq1i/nz57Nr166wm5KzYm272h2sqLQ78h2/IlLcyraSEZFgKGRExCqFjIhYpZAREasUMsCIESO444472LhxIzt37mT9+vXMnz+fysrKsJs2oOuuu44nn3ySHTt2sHXr1rCb06fLLruMV199lffff5+VK1dy/PHHh92kAU2aNIkHH3yQlpYWXNdl+vTpYTcpK9deey2rVq2ivb2d1tZWHnjgAQ4//PDQ2qOQAY444ghisRizZs3i6KOP5qqrrmL27NnceOONYTdtQFVVVdx///3cdtttYTelTxdccAELFizghhtuYPz48TQ3N/PII48wePDgsJvWr5qaGpqbm5kzZ07YTclJQ0MDTU1NTJw4kSlTplBZWcmjjz7KvvvuG1qbXG17b3PnznU3bNgQejuy3WbMmOFu3bo19HZk2lauXOkuXLiw92vHcdzNmze711xzTehty3ZzXdedPn166O3IZxs0aJDruq47adKkUM6vSqYPdXV1bNmyJexmFL3KykomTJjA0qVLe19zXZelS5dy4oknhtq2clFXVwcQ2r9nhUwGhx12GFdccQU//OEPw25K0Rs0aBAVFRW0trbu8XpraysHH3xwaO0qF47jcOutt7JixQrWrl0bShtKOmQaGxtxXbffbcyYMXu8p76+nocffpj777+fO+64o2jaLZJJU1MTY8eO5aKLLgqtDZGf6qEQt9xyC0uWLOl3n40bN/b+eejQoSxbtoynnnqKL37xiwG0MLNc2x1lbW1tdHV1MWTIkD1eHzJkCG+99VZo7SoHCxcu5JxzzmHy5MmhT/wWesdUFLb6+nr3pZdecu+99143FouF3p5ct6h3/H7/+9/v/dpxHHfTpk3q+LW4LVy40N28ebM7atSo0NtS0pVMturr61m+fDmvv/46c+fO3ePWanpfQtQMHz6cAw44gEMPPZR4PM64ceMAWL9+PTt27Ai7eQAsWLCAO++8k2effZZVq1Zx5ZVXUlNTw+LFi8NuWr9qamoYNWpU79cjR45k3LhxbNmyhU2bNoXatv40NTVx8cUXM336dDo6OnqryO3bt/PBBx+E0qbQky7sbcaMGW5fwm7bQNvixYsztruhoSH0tqVuc+bMcV977TX3gw8+cFeuXOmecMIJobdpoK2hoSHjz3bx4sWht62/rS8zZswIpT2a6kFErCrpu0siEj6FjIhYpZAREasUMiJilUJGRKxSyIiIVQoZEbFKISMiVilkRMQqhYyIWKWQERGrFDIiYtV/A/xbzMfcHLsrAAAAAElFTkSuQmCC" + }, + "metadata": {}, + "output_type": "display_data", + "jetTransient": { + "display_id": null + } + } + ], + "execution_count": 26 + }, + { + "cell_type": "markdown", + "id": "ecac7d27-6a72-40ec-a762-b03ef6ca3175", + "metadata": { + "id": "ecac7d27-6a72-40ec-a762-b03ef6ca3175" + }, + "source": [ + "Sólo nos resta evaluar las matrices transpuestas. En el caso de $(AB)^T$, tenemos que\n", + "\n", + "$$(AB)^T = \\begin{pmatrix} 5 & 2 \\\\ 2 & 1\\end{pmatrix}.$$\n" + ] + }, + { + "cell_type": "code", + "id": "83dd6160-8679-4849-98d6-2be1da2ec3a5", + "metadata": { + "id": "83dd6160-8679-4849-98d6-2be1da2ec3a5", + "outputId": "8ed6d146-12b5-459a-bccc-ac0ea616f429", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.617142273Z", + "start_time": "2026-01-31T18:43:11.586161077Z" + } + }, + "source": [ + "(A*B).T" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[5, 2],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}5 & 2\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 27 + }, + { + "cell_type": "markdown", + "id": "8cc29772-781d-46b9-9af1-20d4e20cdfab", + "metadata": { + "id": "8cc29772-781d-46b9-9af1-20d4e20cdfab" + }, + "source": [ + "Por otra parte,\n", + "\n", + "$$B^T A^T = \\begin{pmatrix} 5 & 2 \\\\ 2 & 1\\end{pmatrix}.$$" + ] + }, + { + "cell_type": "code", + "id": "285b5969-0f95-46ec-bdc3-b1668122c7f9", + "metadata": { + "id": "285b5969-0f95-46ec-bdc3-b1668122c7f9", + "outputId": "a8eb1df4-54f0-41a1-b503-2bdd0b100d5f", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.658001287Z", + "start_time": "2026-01-31T18:43:11.625961336Z" + } + }, + "source": "B.T*A.T", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[5, 2],\n", + "[2, 1]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}5 & 2\\\\2 & 1\\end{matrix}\\right]$" + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 28 + }, + { + "cell_type": "markdown", + "id": "65ce9599-42fe-4d90-bc0b-58efc29670d6", + "metadata": { + "id": "65ce9599-42fe-4d90-bc0b-58efc29670d6" + }, + "source": [ + "mientras que\n", + "$$A^T B^T = \\begin{pmatrix} 1 & 2 \\\\ 2 & 5\\end{pmatrix}.$$\n" + ] + }, + { + "cell_type": "code", + "id": "374a319d-1f40-4c81-a03e-ba86cb5d86cc", + "metadata": { + "id": "374a319d-1f40-4c81-a03e-ba86cb5d86cc", + "outputId": "8d5bc463-9e46-4dba-8eea-191f61ab8b40", + "colab": { + "base_uri": "https://localhost:8080/", + "height": 58 + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.690909502Z", + "start_time": "2026-01-31T18:43:11.660057451Z" + } + }, + "source": "A.T*B.T\n", + "outputs": [ + { + "data": { + "text/plain": [ + "Matrix([\n", + "[1, 2],\n", + "[2, 5]])" + ], + "text/latex": "$\\displaystyle \\left[\\begin{matrix}1 & 2\\\\2 & 5\\end{matrix}\\right]$" + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 29 + }, + { + "cell_type": "markdown", + "id": "ccb66e03-3ad0-4a3e-819a-4d78f210f9de", + "metadata": { + "id": "ccb66e03-3ad0-4a3e-819a-4d78f210f9de" + }, + "source": [ + "Entonces," + ] + }, + { + "cell_type": "code", + "id": "01af621c-14ec-4e45-ac16-29c93acad923", + "metadata": { + "id": "01af621c-14ec-4e45-ac16-29c93acad923", + "outputId": "15631aec-0a72-4163-e9a4-86706ba48152", + "colab": { + "base_uri": "https://localhost:8080/" + }, + "ExecuteTime": { + "end_time": "2026-01-31T18:43:11.724827772Z", + "start_time": "2026-01-31T18:43:11.696040095Z" + } + }, + "source": [ + "(A*B).T == B.T*A.T" + ], + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "execution_count": 30 + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.12.12" + }, + "colab": { + "provenance": [] + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}