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diff --git a/sample_notebooks/Raj Kumar/Ch5.ipynb b/sample_notebooks/Raj Kumar/Ch5.ipynb new file mode 100644 index 00000000..5863ba1d --- /dev/null +++ b/sample_notebooks/Raj Kumar/Ch5.ipynb @@ -0,0 +1,402 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 5 - Vectors & Matrices" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.2 Pg 103" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "u+v = [[ 3 -2 4]]\n", + "5*u = [[ 10 15 -20]]\n", + "-v = [[-1 5 -8]]\n", + "2*u-3*v = [[ 1 21 -32]]\n", + "dot product of the two vectors, k = u.v = [[-45]]\n", + "norm or length of the vector u = 5.3852\n" + ] + } + ], + "source": [ + "from __future__ import division\n", + "from numpy import mat\n", + "from numpy.linalg import det\n", + "from numpy import mat, add, dot, multiply, inner\n", + "u=mat([[2,3,-4]])\n", + "v=mat([[1,-5,8]])\n", + "print \"u+v = \",add(u,v)\n", + "print \"5*u = \",multiply(5,u)\n", + "print \"-v = \",multiply(-1,v)\n", + "print \"2*u-3*v = \",add(multiply(2,u),multiply(-3,v))\n", + "print 'dot product of the two vectors, k = u.v = ',inner(u,v)\n", + "from numpy.linalg import norm\n", + "l=norm(u)# \n", + "print 'norm or length of the vector u = ',round(l,4)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.3 Pg 104 " + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2*u-3*v =\n", + "[[ 1]\n", + " [ 9]\n", + " [-2]]\n", + "The dot product of the two vectors u and v is: [[20]]\n", + "norm or length of the vector u = 7.0711\n" + ] + } + ], + "source": [ + "u=mat([[5],[3],[-4]])\n", + "v=mat([[3],[-1],[-2]])\n", + "print \"2*u-3*v =\\n\",add(multiply(2,u),multiply(-3,v))\n", + "print 'The dot product of the two vectors u and v is:', sum(multiply(u,v))\n", + "l=norm(u)#\n", + "print 'norm or length of the vector u = ',round(l,4)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.5 Pg 105" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The addition of the two matrices A and B is:\n", + "[[ 5 4 11]\n", + " [ 1 1 -2]]\n", + "\n", + "The multiplication of a vector with a scalar is:\n", + "[[ 3 -6 9]\n", + " [ 0 12 15]]\n", + "\n", + "2*A-3*B = \n", + "[[-10 -22 -18]\n", + " [ -3 17 31]]\n" + ] + } + ], + "source": [ + "A=mat([[1,-2,3],[0,4,5]])\n", + "B=mat([[4,6,8],[1,-3,-7]])\n", + "k=add(A,B)\n", + "print 'The addition of the two matrices A and B is:\\n',k\n", + "m=multiply(3,A)\n", + "print '\\nThe multiplication of a vector with a scalar is:\\n',m\n", + "p=add(multiply(2,A),multiply(-3,B))\n", + "print \"\\n2*A-3*B = \\n\",p" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.6 Pg 106" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "product of a and b is : [[8]]\n", + "product of p and q is: [[32]]\n" + ] + } + ], + "source": [ + "a=mat([[7,-4,5]])\n", + "b=mat([[3,2,-1]])\n", + "k=inner(a,b)\n", + "print 'product of a and b is : ',k\n", + "p=mat([[6,-1,8,3]])\n", + "q=mat([[4,-9,-2,5]])\n", + "l=inner(p,q)\n", + "print 'product of p and q is:',l" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.7 Pg 107" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A*B = \n", + "[[ 17 -6 14]\n", + " [ -1 2 -14]]\n", + "A*B = \n", + "[[ 5 2]\n", + " [15 10]]\n", + "B*A = \n", + "[[23 34]\n", + " [-6 -8]]\n", + "matrix mulitplication is not commutative since AB may not be equal to BA\n" + ] + } + ], + "source": [ + "A=mat([[1 ,3],[2, -1]])\n", + "B=mat([[2, 0, -4],[5, -2, 6]])\n", + "print \"A*B = \\n\", dot(A,B)\n", + "A=mat([[1, 2],[3, 4]])\n", + "B=mat([[5, 6],[0, -2]])\n", + "print \"A*B = \\n\",dot(A,B)\n", + "print \"B*A = \\n\", dot(B,A)\n", + "print 'matrix mulitplication is not commutative since AB may not be equal to BA'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.8 Pg 109" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "for the function f(x)=2x**2-3x+5,f(A) is :\n", + "[[ 16. -18.]\n", + " [-27. 61.]]\n", + "for the function g(x)=x**2+3x-10,g(A) is\n", + "[[ 0. 0.]\n", + " [ 0. 0.]]\n" + ] + } + ], + "source": [ + "from numpy import identity as idt\n", + "A=mat([[1, 2],[3, -4]])\n", + "A2=dot(A,A) #multiplying A by itself\n", + "A3=dot(A2,A)\n", + "f=add(add(multiply(2,A2),multiply(-3,A)),multiply(5,idt(2)))\n", + "print 'for the function f(x)=2x**2-3x+5,f(A) is :\\n',f\n", + "g=add(add(A2,multiply(3,A)),multiply(-10,idt(2)))\n", + "print 'for the function g(x)=x**2+3x-10,g(A) is\\n',g" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.9 Pg 110" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "A*b = \n", + "[[1 0 0]\n", + " [0 1 0]\n", + " [0 0 1]]\n", + "since A*B is identity matrix,A and B are invertible and inverse of each other\n" + ] + } + ], + "source": [ + "A=mat([[1 ,0 ,2],[2 ,-1, 3],[4, 1, 8]])\n", + "B=mat([[-11, 2 ,2],[-4, 0 ,1],[6, -1, -1]])\n", + "print \"A*b = \\n\",dot(A,B)\n", + "print 'since A*B is identity matrix,A and B are invertible and inverse of each other'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.10 Pg 111" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "determinant of A 7.0\n", + "determinant of B 16.0\n", + "determinant of C -81.0\n" + ] + } + ], + "source": [ + "A=mat([[5 ,4],[2, 3]])\n", + "print 'determinant of A',det(A)\n", + "B=mat([[2, 1],[-4, 6]])\n", + "print 'determinant of B',det(B)\n", + "C=mat([[2, 1, 3],[4, 6, -1],[5 ,1 ,0]])\n", + "print 'determinant of C',det(C)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.13 Pg 115" + ] + }, + { + "cell_type": "code", + "execution_count": 60, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "x = [[ 2.]]\n", + "y = [[-1.]]\n", + "z = [[ 3.]]\n" + ] + } + ], + "source": [ + "A=mat([[1, 2, 1],[2, 5, -1],[3, -2, -1]]) #left hand side of the system of equations\n", + "B=mat([[3] ,[-4] ,[5]]) #right hand side or the constants in the equations\n", + "from numpy import divide\n", + "from numpy.linalg import solve\n", + "X=divide(A,B) # #unique solution for the system of equations\n", + "X = solve(A, B)\n", + "print \"x = \",X[0]\n", + "print \"y = \",X[1]\n", + "print \"z = \",X[2]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ex5.14 Pg 116" + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Inverse of A = \n", + "[[-11. 2. 2.]\n", + " [ -4. 0. 1.]\n", + " [ 6. -1. -1.]]\n" + ] + } + ], + "source": [ + "A=mat([[1 ,0 ,2],[2, -1, 3],[4, 1, 8]])\n", + "A_inv = A**-1\n", + "print \"Inverse of A = \\n\", A_inv" + ] + } + ], + "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 +} |