Crammer's Rule

Crabber's Rule.ipynb

{
 "metadata": {
  "name": "Crammer's Rule"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%pylab inline\n%precision 4",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Populating the interactive namespace from numpy and matplotlib\n"
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def solve(eqs):\n    det = np.linalg.det(np.matrix(map(lambda eq:eq[:-1],eqs)))\n    ans = []\n    for i in range(len(eqs)):\n        mat = []\n        for eq in eqs:\n            row = eq[:-1]\n            row[i] = eq[-1]\n            mat.append(row)\n        ans.append(np.linalg.det(np.matrix(mat))/det)\n    return ans",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$x-2y+z=-3$  \n$x+y-2z=6$  \n$x-y+z=-2$  "
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "solve([[1,-2,1,-3],\n      [1,1,-2,6],\n      [1,-1,1,-2]])",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": "[1.0000, 1.0000, -2.0000]"
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "$x + 2y - 3z + 4w = 12$  \n$2x + 2y - 2z + 3w = 10$  \n$0 + y + z + 0 = -1$  \n$x - y + z - 2w = -4$  "
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "solve([[1,2,-3,4,12],\n       [2,2,-2,3,10],\n       [0,1,1,0,-1],\n       [1,-1,1,-2,-4]])",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": "[1.0000, -0.0000, -1.0000, 2.0000]"
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}