{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "A = np.array([[1, -1, -1],\n",
    "              [3, -3, 2],\n",
    "              [2, -1, 1]])\n",
    "b = [2, 16, 9]\n",
    "\n",
    "np.linalg.solve(A, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "A = np.array([[1, -1, -1],\n",
    "              [3, -3, 2],\n",
    "              [2, -1, 1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x1 = np.linalg.solve(A, [1, 0, 0])\n",
    "x1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x2 = np.linalg.solve(A, [0, 1, 0])\n",
    "x2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "x3 = np.linalg.solve(A, [0, 0, 1])\n",
    "x3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Ainv = np.array([x1, x2, x3]).T\n",
    "Ainv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "A = np.array([[1, -1, -1],\n",
    "              [3, -3, 2],\n",
    "              [2, -1, 1]])\n",
    "\n",
    "Ainv = np.linalg.inv(A)\n",
    "Ainv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "A@Ainv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.linalg.inv(A)@b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%timeit np.linalg.inv(A)@b\n",
    "%timeit np.linalg.solve(A, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Singular matrix!\n",
    "A = np.array([[4, 2],\n",
    "              [8, 4]])\n",
    "\n",
    "Ainv = np.linalg.inv(A)\n",
    "Ainv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.linalg.solve(A, [1, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.linalg.solve(A, [0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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",
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 "nbformat": 4,
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}