{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Chapter 4 Determinants"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.3.1 Pg:210"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Determinant= -0.0288448892628\n"
     ]
    }
   ],
   "source": [
    "from numpy.linalg import det\n",
    "from numpy.random import rand\n",
    "n= 4 # the value of n\n",
    "a=rand(n,n)\n",
    "determinant = det(a)\n",
    "print 'Determinant=',determinant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.3.3 Pg: 214"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A=\n",
      "[[ 2 -1  0  0]\n",
      " [-1  2 -1  0]\n",
      " [ 0 -1  2 -1]\n",
      " [ 0  0 -1  2]]\n",
      "[[ 5.]]\n"
     ]
    }
   ],
   "source": [
    "from numpy import mat,shape, transpose as tp\n",
    "from numpy.linalg import det\n",
    "A=[[2, -1, 0, 0],[-1, 2, -1, 0],[0, -1 ,2 ,-1],[0, 0 ,-1 ,2]]\n",
    "A=mat(A)\n",
    "print 'A=\\n',A\n",
    "m,n=shape(A)\n",
    "\n",
    "a=A[1,:]\n",
    "\n",
    "c=[];\n",
    "for L in range(0,4):\n",
    "    \n",
    "    for i in range(0,4):\n",
    "        l=[]\n",
    "        for j in range(0,4):\n",
    "            if i!=j:\n",
    "                l.append(j)\n",
    "            \n",
    "        B=A[1:4,l]\n",
    "        \n",
    "    \n",
    "    c1l=(-1)**(1+L+1)*det(B);\n",
    "    c=c+[c1l]\n",
    "\n",
    "d=a*tp(mat(c))+1;\n",
    "print d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.4.1 Pg:282"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Adjoint of A:\n",
      "[[ 1. -1.  0.]\n",
      " [ 0.  1. -1.]\n",
      " [ 0.  0.  1.]]\n",
      "inv(A):\n",
      "[[ 1. -1.  0.]\n",
      " [ 0.  1. -1.]\n",
      " [ 0.  0.  1.]]\n"
     ]
    }
   ],
   "source": [
    "# inverse of a sum matrix is a difference matrix\n",
    "from numpy import mat,linalg,dot\n",
    "A=mat([[1, 1 ,1],[0, 1, 1],[0, 0, 1]])\n",
    "adjA = linalg.det(A)*linalg.inv(A)*linalg.det(A)\n",
    "invA=(adjA/det(A))\n",
    "print 'Adjoint of A:\\n',adjA\n",
    "print 'inv(A):\\n',invA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ex:4.4.2 Pg: 222"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x1= 9.0\n",
      "x2= -3.0\n"
     ]
    }
   ],
   "source": [
    "from numpy import mat\n",
    "from numpy.linalg import det\n",
    "#x1+3x2=0\n",
    "#2x1+4x2=6\n",
    "A=mat([[1, 3],[2, 4]])\n",
    "b=mat([[0],[6]])\n",
    "X1=mat([[0, 3],[6, 4]])\n",
    "X2=mat([[1, 0],[2, 6]])\n",
    "print 'x1=',(det(X1)/det(A))\n",
    "print 'x2=',(det(X2)/det(A))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}