LA_Ch01_02_Ex03.ipynb

la_ch01_02_ex03.ipynb

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      "name": "python3",
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      "name": "python"
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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/gist/dsaint31x/72fa6d150b869c561eded8f745004913/la_ch01_02_ex03.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "cell_type": "code",
      "source": [
        "import sympy as sp\n",
        "\n",
        "def custom_latex_printer(exp, **options):\n",
        "    from google.colab.output._publish import javascript\n",
        "    url = \"https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/latest.js?config=default\"\n",
        "    javascript(url=url)\n",
        "    return sp.printing.latex(exp, **options)\n",
        "\n",
        "sp.init_printing(use_latex=\"mathjax\", latex_printer=custom_latex_printer)"
      ],
      "metadata": {
        "id": "Ci5iemI-WHkq"
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      "execution_count": 29,
      "outputs": []
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      "cell_type": "code",
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      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "<script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.3/latest.js?config=default'></script>"
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          "data": {
            "text/plain": [
              "⎛⎡1  0  -2.0  3.0  0  -24.0⎤           ⎞\n",
              "⎜⎢                         ⎥           ⎟\n",
              "⎜⎢0  1  -2.0  2.0  0  -7.0 ⎥, (0, 1, 4)⎟\n",
              "⎜⎢                         ⎥           ⎟\n",
              "⎝⎣0  0   0     0   1   4.0 ⎦           ⎠"
            ],
            "text/latex": "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & -2.0 & 3.0 & 0 & -24.0\\\\0 & 1 & -2.0 & 2.0 & 0 & -7.0\\\\0 & 0 & 0 & 0 & 1 & 4.0\\end{matrix}\\right], \\  \\left( 0, \\  1, \\  4\\right)\\right)$"
          },
          "metadata": {},
          "execution_count": 30
        }
      ],
      "source": [
        "import numpy as np\n",
        "import sympy as sp\n",
        "\n",
        "A = np.array([\n",
        "    [0 , 3, -6, 6, 4,-5],\n",
        "    [3 ,-7 , 8,-5, 8, 9],\n",
        "    [3 ,-9 ,12,-9, 6,15]\n",
        "], dtype=float)\n",
        "\n",
        "A = sp.Matrix(A)\n",
        "rref_A = A.rref()\n",
        "rref_A # rref and pivot columns\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "np.array(rref_A[0].tolist(), dtype=float)"
      ],
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        "id": "jBGbf72LGAuJ",
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      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[  1.,   0.,  -2.,   3.,   0., -24.],\n",
              "       [  0.,   1.,  -2.,   2.,   0.,  -7.],\n",
              "       [  0.,   0.,   0.,   0.,   1.,   4.]])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    }
  ]
}