linearalgebra_practice101hw.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style>\n",
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   "source": [
    "%%html\n",
    "<style>\n",
    "@import url('https://fonts.googleapis.com/css?family=Roboto&effect=3d|brick-sign|');\n",
    "span {font-family:Roboto; color:black; text-shadow:4px 4px 4px #aaa;}  \n",
    "h1,h2 {font-family:Roboto; color:slategray; text-shadow:4px 4px 4px #aaa;} \n",
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    "</style> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy\n",
    "sympy.init_printing(use_unicode=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задачи / Problems\n",
    "[Проскуряков И.В. Сборник задач по линейной алгебре](http://elibrary.sgu.ru/uch_lit/560.pdf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Перестановки и подстановки\n",
    "### #125 \n",
    "1, 9, 6, 3, 2, 5, 4, 7, 8\n",
    "\n",
    "---\n",
    "- (9,6), (9,3), (9,2), (9,5), (9,4), (9,7), (9,8) - 7\n",
    "- (6,3), (6,2), (6,5), (6,4) - 4\n",
    "- (5,4) - 1\n",
    "- (3,2) - 1\n",
    "\n",
    "7 + 4 + 1 + 1 = 13\n",
    "\n",
    "### #126 \n",
    "7, 5, 6, 4, 1, 3, 2\n",
    "\n",
    "---\n",
    "- (7,5), (7,6), (7,4), (7,1), (7,3), (7,2) - 6\n",
    "- (6,4), (6,1), (6,3), (6,2) - 4\n",
    "- (5,4), (5,1), (5,3), (5,2) - 4\n",
    "- (4,1), (4,3), (4,2) - 3\n",
    "- (3,2) - 1\n",
    "\n",
    "6 + 4 + 4 + 3 + 1 = 18"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### # 189\n",
    "$a_{61}a_{23}a_{45}a_{36}a_{12}a_{54} = a_{12}a_{23}a_{36}a_{45}a_{54}a_{61}$\n",
    "\n",
    "1 2 3 4 5 6\n",
    "\n",
    "2 3 6 5 4 1\n",
    "\n",
    "- (6,5), (6,4), (6,1) - 3\n",
    "- (5,4), (5,1) - 2\n",
    "- (4,1) - 1\n",
    "- (3,1) - 1\n",
    "- (2,1) - 1\n",
    "\n",
    "3 + 2 + 1 + 1 + 1 = 8 - четное / even => \"+\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### # 190\n",
    "$a_{27}a_{36}a_{51}a_{74}a_{25}a_{43}a_{62} = a_{25}a_{27}a_{36}a_{43}a_{51}a_{62}a_{74}$\n",
    "\n",
    "a_{25}a_{27} => не является слагаемым определителя / is not a summand of the determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}4 & -1\\\\5 & -2\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡4  -1⎤\n",
       "⎢     ⎥\n",
       "⎣5  -2⎦"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 800\n",
    "A800 = sympy.Matrix([[4,-1], [5,-2]])\n",
    "A800"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}11 & -2\\\\10 & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡11  -2⎤\n",
       "⎢      ⎥\n",
       "⎣10  -1⎦"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A800 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}11 & -2\\\\10 & -1\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡11  -2⎤\n",
       "⎢      ⎥\n",
       "⎣10  -1⎦"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A800_2 = sympy.Matrix([[4 * 4 - 1 * 5, 4 * (-1) - 1 * (-2)], [5 * 4 - 2 * 5, 5 * (-1) - 2 * (-2)]])\n",
    "A800_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}101 & -20\\\\100 & -19\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡101  -20⎤\n",
       "⎢        ⎥\n",
       "⎣100  -19⎦"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A800 ** 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left ( \\left[\\begin{matrix}101 & -20\\\\100 & -19\\end{matrix}\\right], \\quad \\left[\\begin{matrix}4 & -1\\\\5 & -2\\end{matrix}\\right]\\right )$$"
      ],
      "text/plain": [
       "⎛⎡101  -20⎤  ⎡4  -1⎤⎞\n",
       "⎜⎢        ⎥, ⎢     ⎥⎟\n",
       "⎝⎣100  -19⎦  ⎣5  -2⎦⎠"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A800_4 = sympy.Matrix([[11 * 11 - 2 * 10, 11 * (-2) - 2 * (-1)], [10 * 11 - 1 * 10,  10 * (-2) - 1 * (-1)]])\n",
    "A800_4, A800"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAAzBAMAAAB8hdsWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEN2ZRGYiibtUds3vMqtNptRAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACeUlEQVRIDe2Wz2vTYBjHv12TNu3StPEiyCChcwcvs1LxMhwF7zLwD7A4VPCyiofBLlYQhIHQ/2DbdQwNigcRtYJnFxTxaEFELxuLOrVDic/b5M3Pt7jOgyA+hzR9n+eTp+/7Jp8Guq5jhMjoegXH3c8jIFBct42joxCsVj44c/naTSC/dIpd5hU7pGNx0QZeVijh9cnUcL6DhzjUpKHpdD2NXGhoZubd05Ap9mFYsol8GyiKmftQKHk3ZKTnKFtKDwUHeP1E1IdlKCIMfVuZK9cg9YGWkBnvMiTOSFMwiNlFsSlkyo+XTiaY0p0tLLRQ2sNFCBnjAdROog9WOoz5htYQZgfZZ0lGdYwWpD25GWcy96os7LIJ+UuMKdlQ+rQGhf4VxJnBzOkwZkHejTGGQwytv+yc3d7+8YEXRj6VVB+1B9WRu8haVPYiUhqcSjSfbqyPPEf7g2OYsKnoe1AYPbmFicS6nanTPXp4fYuqZtzlaC0/z9cp+XFzepXfozyxv88/eH7218Cv+t/nL+6PjUzzN7vl70/oxM1H1YqQYU6cn7lNOY+JOLH66aoQYU7M9XC9wZmIE3tCAmBO1CpQu5yJOHEIM3Ci6kD7yhm6NnfiEGbgRM2E9jNkAie+Xz9NV0iF70SM7QRM6MQbWGikCMB3It6uBgz9Nt+JACkmHYbnRExSKnh+fCfSUJamGUTCidkaZTwmdKJiIUvTTIXvxHMs4TGhE1VaGppmKjwnFlq4xJnQiXlAbacIwHPiG2CNM6ETczVsCO835sTcZH3W5AxCJ87PnhC0oT91cuK467pWwAjLhg0Gaz2sQDD+DzJTo77zHWkf5J3vF/ze3sjBvulDAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}304 & -61\\\\305 & -62\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡304  -61⎤\n",
       "⎢        ⎥\n",
       "⎣305  -62⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A800 ** 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGUAAAAzBAMAAAB8hdsWAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEN2ZRGYiibtUds3vMqtNptRAAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACeUlEQVRIDe2Wz2vTYBjHv12TNu3StPEiyCChcwcvs1LxMhwF7zLwD7A4VPCyiofBLlYQhIHQ/2DbdQwNigcRtYJnFxTxaEFELxuLOrVDic/b5M3Pt7jOgyA+hzR9n+eTp+/7Jp8Guq5jhMjoegXH3c8jIFBct42joxCsVj44c/naTSC/dIpd5hU7pGNx0QZeVijh9cnUcL6DhzjUpKHpdD2NXGhoZubd05Ap9mFYsol8GyiKmftQKHk3ZKTnKFtKDwUHeP1E1IdlKCIMfVuZK9cg9YGWkBnvMiTOSFMwiNlFsSlkyo+XTiaY0p0tLLRQ2sNFCBnjAdROog9WOoz5htYQZgfZZ0lGdYwWpD25GWcy96os7LIJ+UuMKdlQ+rQGhf4VxJnBzOkwZkHejTGGQwytv+yc3d7+8YEXRj6VVB+1B9WRu8haVPYiUhqcSjSfbqyPPEf7g2OYsKnoe1AYPbmFicS6nanTPXp4fYuqZtzlaC0/z9cp+XFzepXfozyxv88/eH7218Cv+t/nL+6PjUzzN7vl70/oxM1H1YqQYU6cn7lNOY+JOLH66aoQYU7M9XC9wZmIE3tCAmBO1CpQu5yJOHEIM3Ci6kD7yhm6NnfiEGbgRM2E9jNkAie+Xz9NV0iF70SM7QRM6MQbWGikCMB3It6uBgz9Nt+JACkmHYbnRExSKnh+fCfSUJamGUTCidkaZTwmdKJiIUvTTIXvxHMs4TGhE1VaGppmKjwnFlq4xJnQiXlAbacIwHPiG2CNM6ETczVsCO835sTcZH3W5AxCJ87PnhC0oT91cuK467pWwAjLhg0Gaz2sQDD+DzJTo77zHWkf5J3vF/ze3sjBvulDAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}304 & -61\\\\305 & -62\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡304  -61⎤\n",
       "⎢        ⎥\n",
       "⎣305  -62⎦"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A800_5 = sympy.Matrix([[101 * 4 - 20 * 5, 101 * (-1) - 20 * (-2)], [100 * 4 - 19 * 5, 100 * (-1)  - 19 * (-2)]])\n",
    "A800_5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Типовой расчет 1 / Standard Calculation 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Постановка  задачи / Formulation of the problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$ \n",
       "G = \\alpha * A * B^T \\ + \\ \\beta * C * D; \\\\\n",
       "\\\\\n",
       "\\alpha = 2, \\ \\beta = -5, \\\\ \n",
       "\n",
       "A_{(2,3)} = \n",
       " \\begin{pmatrix}\n",
       "-3 & -3 & -6 \\\\\n",
       "-4 & -7 & 8 \\\\\n",
       " \\end{pmatrix}, \\ \n",
       "\n",
       "B_{(4,3)} = \n",
       " \\begin{pmatrix}\n",
       "2 & 8 & 7 \\\\\n",
       "-5 & -6 & -2 \\\\\n",
       "-8 & 4 & -8 \\\\\n",
       "7 & 4 & -6 \\\\\n",
       " \\end{pmatrix}, \\ \n",
       "\n",
       "C_{(2,2)} = \n",
       " \\begin{pmatrix}\n",
       "-2 & -4 \\\\\n",
       "3 & -5 \\\\\n",
       " \\end{pmatrix}, \\ \n",
       "\n",
       "D_{(2,4)} = \n",
       " \\begin{pmatrix}\n",
       "-2 & -3 & -1 & 3 \\\\\n",
       "-2 & -9 & 8 & 9 \\\\\n",
       " \\end{pmatrix}.\n",
       "$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%latex\n",
    "$ \n",
    "G = \\alpha * A * B^T \\ + \\ \\beta * C * D; \\\\\n",
    "\\\\\n",
    "\\alpha = 2, \\ \\beta = -5, \\\\ \n",
    "\n",
    "A_{(2,3)} = \n",
    " \\begin{pmatrix}\n",
    "-3 & -3 & -6 \\\\\n",
    "-4 & -7 & 8 \\\\\n",
    " \\end{pmatrix}, \\ \n",
    "\n",
    "B_{(4,3)} = \n",
    " \\begin{pmatrix}\n",
    "2 & 8 & 7 \\\\\n",
    "-5 & -6 & -2 \\\\\n",
    "-8 & 4 & -8 \\\\\n",
    "7 & 4 & -6 \\\\\n",
    " \\end{pmatrix}, \\ \n",
    "\n",
    "C_{(2,2)} = \n",
    " \\begin{pmatrix}\n",
    "-2 & -4 \\\\\n",
    "3 & -5 \\\\\n",
    " \\end{pmatrix}, \\ \n",
    "\n",
    "D_{(2,4)} = \n",
    " \\begin{pmatrix}\n",
    "-2 & -3 & -1 & 3 \\\\\n",
    "-2 & -9 & 8 & 9 \\\\\n",
    " \\end{pmatrix}.\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Решение / Decisions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "α, β = 2, -5\n",
    "A = sympy.Matrix([[-3, -3, -6], [-4, -7, 8]])\n",
    "B = sympy.Matrix([[2, 8, 7], [-5, -6, -2], [-8, 4, -8], [7, 4, -6]])\n",
    "C = sympy.Matrix([[-2, -4], [3, -5]])\n",
    "D = sympy.Matrix([[-2, -3, -1, 3], [-2, -9, 8, 9]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAKgAAABLCAMAAADTRTyqAAAAOVBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACXHtMAAAAEnRSTlMAMquJZkQiEEAwmc277912VHz2pxcrAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEEklEQVRoBe2b0ZajIAyGFSzuoqLL+z/sEhA7gSChetE9KxdjCzF8BqTwn0zXW19E96XFBL6u660cXHl9KWcHcIOwAKo+Y+zhtvHDm0tdqmGkmgYEqrSeZt89ZZvVLXaajCH9ZrauYpSr1NVx28JA2wW7QKAKpqm0VV/RhTHWSDZnp+E+scW7C1c5Ce2KSewQqPCdLsmzFBxCp+UmomUYoHKciKafVf5xOhUu7wYEulggFewp2wYqZ+i2ChoimblGoMKAK2G5szTzBrcXy8vOLg7ax7VotDfIDAGBBivj3i9eEcO66sxl8V5h7aqTqUcbKx981JaD9nZFFidfIEKK/+6599ROrMVM5O9zDmrSaXxCCk2zny8VI9+8STVbznMpYkwzUF3mHN2ieZRjxHXp3UvNB/C82cUvLacPJomVIQX13k69vBtn709z371AqGx9lpp8inYJ6CYdh2LNo65b9kXijX72adzHU1Rf+9ESywkG7YGzW+uD44m8cbcQj08CL+H552oYXpaYfghUGfjxCqsp2Reu9L8eK2POhdteEwRgqK8pmw0hQL0h0CnsB4ipjO45vrg9jNDM8LubevgRzxeew138oBZiGiPQaPmN1wf07lF5IvpE9O4I3O3vmaNPRO+OwN3+8BzlSQQ/GKQrxxb6R332sSc2RJnRuyI3x6DeW1UiOPwp47YYvM2WIbaYh5/8Q26OQJkSweF3ggebOfvRNe/58EJ8IMwRKFMiiJ43r1fEb2fXfphaIkqZI9AWicBxTWztR3ZNoJQ5AnUiCVcigPjZqZcrZye8qiZQ0hyD8iUCxznaCc5p1HYcHuNdlDNriChtjkHZEgFQjNafK3X10AQnoAZQ2hyBViSCVFGw/rg81LSPAY6dfNCCOYD+sr8hQm4U/UGNIxF4c+NPgYM9P6grf+xkg5bM/zjQqOHzJQLPuatOtYi+BBS7COIMHPygvyVzNPRsiSC4fu1zFHVU+LK0rKNubDNzBMqWCHaa2QVprL/1YG05v1/vh8zNEShbIogepVMgOHsS7aSNuS6RRLeUOQaNll94fUDvHpQnok9E747A3f6eOfpEFCJQSD64Ozgf+UNztJB8UHTcmDBxSd5AoIXkgxJoa8LEJXkDgQbZJUs+KIE2JkxckzcQaCH5oATamDBxTd5AoJ6IJ3qBaWPCxDV5IwMlkg9KEQ31DQkTV+SNDJRIPjgFbUiYuCRvpKBU8sEpaEPCxCV5IwWlkg8iaCpAQH1DwsQ1eSMFpZIPIihxbUmYuCZvJKBk8gEBuFe1JExclDcSUDL5oAjaljBxTd5IQMnkgxJoY8LENXkjASWTD0qgrQkT3AyI2B+SNxLQaPN91wf07jF5IvqfR/Qf+YeB0Wfkf/k/DLiDzF9Opi7HOi1a7QAAAABJRU5ErkJggg==\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}2 & -5 & -8 & 7\\\\8 & -6 & 4 & 4\\\\7 & -2 & -8 & -6\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡2  -5  -8  7 ⎤\n",
       "⎢             ⎥\n",
       "⎢8  -6  4   4 ⎥\n",
       "⎢             ⎥\n",
       "⎣7  -2  -8  -6⎦"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-72 & 45 & 60 & 3\\\\-8 & 46 & -60 & -104\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-72  45  60    3  ⎤\n",
       "⎢                  ⎥\n",
       "⎣-8   46  -60  -104⎦"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A * B.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAO0AAAAzBAMAAACJV5LjAAAAMFBMVEX///8AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAEN2ZRGbNMqt2u++JIlQ+K2npAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAEHElEQVRYCe1YzWtUVxT/TWZunK98TAtFUZjRWKsbO5ASBFFm2V0D/QM6rUgFUYNFCFQwtkhtKZjSVUFwKBTxCxJw4UoHXIgQcGhxoSBmWxBM/EiI1TzPPe9+vTd3XlaTdDF3ce6553fO+eXed1/ej0GpVMI6j1SpNIxPg5frTIt8EDSwc71ZJZ/4n/CeHJZ/zXfGSIdHevQsULx/QK/tLEv+GbvcATV5c3MTxo/vN/XjCebdLTPY6NTUHnzfwnF80NIRNXPJwBQe1HyoTf67lq3YFUTsnC9J3pykZENzOLIzyFdFBcWGjpiZSrLDKMz4UZ12CHm3VPh4Tx2hbDa6CkN1FBfyUxhcNCHtEG9hEdl3flRlxeuEj7cpedno3ig3kFseqiKzakLakfutINsBVVn9Mzo9nIWHN9ciXjY2V+73VZl4X9uY8vjRoG/Bj6qkoW/vf+ZWCg/vQxAvG5spn+/rp01sWrEx5YW8Z6b9qEoqH0Zh3ikVHt6m5GVjE1M3MbkqO7+1MeWFvCPwoyqpvID0rFMqmDf1zQ45JgBqIlrEy8bJw4cX/10uN5FZcYPsM2+6Cj+q0ocqEK+cUtG+30cgXjZOHrnpRbpXg957BXwJ+FHVo68O4V4ND+/n58//9yubKG9/g95A4X2PMNjEEz+qeuTX3i9l3pLZbFQZBmfxdELMIF3XETPLcz4N/OZHVVqGnq/7Kon2c6bMNzKbjXTkyG3HX8BebKU7EBvEOzAyuq/iR3XydWyd1z7NIsr7y53d08BYcEUZmzl3twZs++MnG1GeLOkPgqDuRU16cTRSKqK8Jq3bTo+32ycc9u+dc++cu3ECvXu1aTuda3HuXux0WbezPI8BvFxTu1thv+2iFFoi/v958xh9YQd24gfuZwzr9gGW5yZmnLW1e1jJsr+K7LyHFzni7a/iqunKDut2lufRuFrRtzBRu1tQjCNV78T7nD7l0cG6neV5NK5WxJuo3S1YbCTwHm1rzro9K+V5GyQDcr9J2t2CmTfD6fFO+106/Xst2p91O4X6FqJxtSJeBhO0uxb2F1YOUqqI3yv5fFNL47hNoDNYt9P6zLQTtG7Im6jdNVgMjlGd8PIGwH7egenMup1WIyYScULeRO2uwWePg5rD+xEr909IwdF9fgF8RaA7pG4nDV11YxG5z2Bcu9sMLexFFc9nHV7TT/LuIt5xE1FOmgCS597B+03U7hoskPok7S9854w/2/dLL3WD5XlH3kTtbsAy1Z/rxPsFPd9of9btLM+jcbWS+03U7gYstIAbnXjzzVTsPrNuD+W5j5h4E7W7BTNfQ0x7eLPXXvwM3N03EWsvdXsoz2OAXK6p3R1hPznq/S54unYjJNruVTdY2nv2eNvPpBuRDTznjzfid+8tjY363fs9d/V3IO8i5OcAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-144 & 90 & 120 & 6\\\\-16 & 92 & -120 & -208\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-144  90  120    6  ⎤\n",
       "⎢                    ⎥\n",
       "⎣-16   92  -120  -208⎦"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "α * A * B.transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}12 & 42 & -30 & -42\\\\4 & 36 & -43 & -36\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡12  42  -30  -42⎤\n",
       "⎢                ⎥\n",
       "⎣4   36  -43  -36⎦"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "C * D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-60 & -210 & 150 & 210\\\\-20 & -180 & 215 & 180\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-60  -210  150  210⎤\n",
       "⎢                   ⎥\n",
       "⎣-20  -180  215  180⎦"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "β * C * D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$$\\left[\\begin{matrix}-204 & -120 & 270 & 216\\\\-36 & -88 & 95 & -28\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡-204  -120  270  216⎤\n",
       "⎢                    ⎥\n",
       "⎣-36   -88   95   -28⎦"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "G = α * A * B.transpose() + β * C * D\n",
    "G"
   ]
  }
 ],
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