Linalg_as_matrices.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "273eea70-bc7e-4a81-aab0-eeec304d1d5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from utils import plot_lines"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "63a9fa7a-e2b3-4649-ab4e-f334a88b3da9",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{cases} \n",
    "-x_1+3x_2=7, \\\\ 3x_1+2x_2=1, \\end{cases}\\tag{1}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24fa9980-7b96-4812-869f-9656af3f1e96",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{bmatrix}\n",
    "-1 & 3 & 7 \\\\\n",
    "3 & 2 & 1\n",
    "\\end{bmatrix}\n",
    "$$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "43de595c-7e91-4c22-8145-1fab7aee8084",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix A:\n",
      "[[-1.  3.]\n",
      " [ 3.  2.]]\n",
      "\n",
      "Array b:\n",
      "[7. 1.]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([\n",
    "        [-1, 3],\n",
    "        [3, 2]\n",
    "    ], dtype=np.dtype(float))\n",
    "\n",
    "b = np.array([7, 1], dtype=np.dtype(float))\n",
    "\n",
    "print(\"Matrix A:\")\n",
    "print(A)\n",
    "print(\"\\nArray b:\")\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379d95af-a982-483e-9e57-0e1ff4215220",
   "metadata": {},
   "source": [
    "### shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "6fc3416c-194c-4d36-be8d-d2e1a0c35949",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Shape of A: (2, 2)\n",
      "Shape of b: (2,)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Shape of A: {A.shape}\")\n",
    "print(f\"Shape of b: {b.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8c7d898-dbbf-436b-8f07-2c61541d2086",
   "metadata": {},
   "source": [
    "### solve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7936eb79-2f6a-4ca5-a764-3d061ba1004a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Solution: [-1.  2.]\n"
     ]
    }
   ],
   "source": [
    "x = np.linalg.solve(A, b)\n",
    "print(f\"Solution: {x}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceff829b-b003-4b94-8418-a6d5041e74f6",
   "metadata": {},
   "source": [
    "### Determinant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c9758e4c-7edb-4a0c-8af4-f62b1a3672e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Determinant of matrix A: -11.00\n"
     ]
    }
   ],
   "source": [
    "d = np.linalg.det(A)\n",
    "print(f\"Determinant of matrix A: {d:.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bb8e1112-5d6f-42a7-91a2-c9cd7ff3cb00",
   "metadata": {},
   "source": [
    "### Representation of the system as a matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "d1be17b5-d9d6-4ced-ace3-148b78fa6370",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-1.  3.  7.]\n",
      " [ 3.  2.  1.]]\n"
     ]
    }
   ],
   "source": [
    "A_system = np.hstack((A, b.reshape((2, 1))))\n",
    "print(A_system)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1e528b05-dc92-4d47-923e-7206653d5af0",
   "metadata": {},
   "source": [
    "### Graphical Representation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1248e925-429a-49b3-bea1-002bc3418058",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x1000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_lines(A_system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "72b2b10f-205f-4c99-bbc2-a6de3be4b190",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected Jupyter core packages...\n",
      "IPython          : 8.25.0\n",
      "ipykernel        : 6.28.0\n",
      "ipywidgets       : 8.1.2\n",
      "jupyter_client   : 8.6.0\n",
      "jupyter_core     : 5.5.0\n",
      "jupyter_server   : 2.10.0\n",
      "jupyterlab       : 4.2.3\n",
      "nbclient         : 0.8.0\n",
      "nbconvert        : 7.10.0\n",
      "nbformat         : 5.9.2\n",
      "notebook         : 7.2.1\n",
      "qtconsole        : 5.5.1\n",
      "traitlets        : 5.14.3\n"
     ]
    }
   ],
   "source": [
    "!jupyter --version"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "example",
   "language": "python",
   "name": "example"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}