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+{
+"cells": [
+ {
+		   "cell_type": "markdown",
+	   "metadata": {},
+	   "source": [
+       "# Chapter 7: Numerical Solutions for Matrix Inversion"
+	   ]
+	},
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.1: Gauss_Jordan_Two_Array_Method.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.1\n",
+"//Gauss-Jordan Two Array Method\n",
+"//Page no. 254\n",
+"clc;clear;close;\n",
+"\n",
+"A=[2,6,1;3,9,2;0,-1,3];   //matrix\n",
+"C=eye(3,3);               //Unit Matrix\n",
+"for i=1:3                  //interchange of row 1 and 2\n",
+"    B(1,i)=A(1,i);\n",
+"    A(1,i)=A(2,i);\n",
+"    A(2,i)=B(1,i);\n",
+"    B(2,i)=C(1,i);\n",
+"    C(1,i)=C(2,i);\n",
+"    C(2,i)=B(2,i);\n",
+"end\n",
+"printf('\n')\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"\n",
+"for i=1:3\n",
+"    A(1,i)=A(1,i)/3;\n",
+"    C(1,i)=C(1,i)/3;\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(2,i)=A(2,i)-2*A(1,i);\n",
+"    C(2,i)=C(2,i)-2*C(1,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3        //interchange of row 2 and 3\n",
+"    B(1,i)=A(2,i);\n",
+"    A(2,i)=A(3,i);\n",
+"    A(3,i)=B(1,i);\n",
+"    B(2,i)=C(2,i);\n",
+"    C(2,i)=C(3,i);\n",
+"    C(3,i)=B(2,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(2,i)=-1*A(2,i);\n",
+"    C(2,i)=-1*C(2,i);\n",
+"end\n",
+"for i=1:3\n",
+"    A(1,i)=A(1,i)-3*A(2,i);\n",
+"    C(1,i)=C(1,i)-3*C(2,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(3,i)=-3*A(3,i);\n",
+"    C(3,i)=-3*C(3,i);\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"for i=1:3\n",
+"    A(1,i)=A(1,i)-A(3,i)*(29/3);\n",
+"    C(1,i)=C(1,i)-29*C(3,i)/3;\n",
+"end\n",
+"for i=1:3\n",
+"    A(2,i)=A(2,i)+A(3,i)*3;\n",
+"    C(2,i)=C(2,i)+C(3,i)*3;\n",
+"end\n",
+"\n",
+"//printing of matrices A and C\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        printf('%f\t',A(i,j))\n",
+"    end\n",
+"    printf('|\t');\n",
+"    for j=1:3\n",
+"        printf('%f\t',C(i,j))\n",
+"    end\n",
+"    printf('\n')\n",
+"end\n",
+"printf('\n\n');\n",
+"\n",
+"disp(C,'Inverse Matrix of A')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.2: Inverse_in_Place_without_Pivoting.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.2\n",
+"//Inverse in Place without Pivoting\n",
+"//Page no. 256\n",
+"clc;clear;close;\n",
+"\n",
+"A=[3,-6,7;9,0,-5;5,-8,6];   //matrix\n",
+"B=[3,-6,7;9,0,-5;5,-8,6];   //copied matrix\n",
+"for i=1:3\n",
+"    printf('\n\nStage %i',i);\n",
+"    for j=1:3\n",
+"        if(i==j)\n",
+"            B(i,j)=1/B(i,j);\n",
+"        else\n",
+"            B(i,j)=A(i,j)/A(i,i);\n",
+"        end,\n",
+"    end\n",
+"    disp(B)\n",
+"        for j=1:3\n",
+"            for k=1:3\n",
+"                if(i~=j)\n",
+"                    B(j,k)=A(j,k)-A(j,i)*B(i,k);\n",
+"                end,\n",
+"            end\n",
+"        end\n",
+"        disp(B)\n",
+"    for j=1:3\n",
+"        if(i~=j)\n",
+"            B(j,i)=-1*A(j,i)*B(i,i);\n",
+"        end,\n",
+"        \n",
+"    end\n",
+"    disp(B)\n",
+"    A=B;\n",
+"end\n",
+"disp(B,'Inverse of Matrix A=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.3: Inverse_in_Place_with_Pivoting.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.3\n",
+"//Inverse in Place with Pivoting\n",
+"//Page no. 258\n",
+"clc;clear;close;\n",
+"\n",
+"A=[3,-6,7;9,0,-5;5,-8,6];     //matrix\n",
+"B=[3,-6,7;9,0,-5;5,-8,6];      //copied matrix\n",
+"\n",
+"for i=1:3\n",
+"    printf('\n\nStage %i',i)\n",
+"    if(i<3)\n",
+"        for j=1:3         //interchange of rows\n",
+"            C(i,j)=A(i,j);\n",
+"            A(i,j)=A(i+1,j);\n",
+"            A(i+1,j)=C(i,j);\n",
+"            C(i,j)=B(i,j);\n",
+"            B(i,j)=B(i+1,j);\n",
+"            B(i+1,j)=C(i,j);\n",
+"        end\n",
+"    end\n",
+"    disp(B)\n",
+"    for j=1:3\n",
+"        if(i==j)\n",
+"            B(i,j)=1/B(i,j);\n",
+"        else\n",
+"            B(i,j)=A(i,j)/A(i,i);\n",
+"        end,\n",
+"    end\n",
+"        for j=1:3\n",
+"            for k=1:3\n",
+"                if(i~=j)\n",
+"                    B(j,k)=A(j,k)-A(j,i)*B(i,k);\n",
+"                end,\n",
+"            end\n",
+"        end\n",
+"    for j=1:3\n",
+"        if(i~=j)\n",
+"            B(j,i)=-1*A(j,i)*B(i,i);\n",
+"        end,\n",
+"        \n",
+"    end\n",
+"    disp(B)\n",
+"    A=B;\n",
+"end\n",
+"for j=1:3      //interchange of column 2 and 3\n",
+"    C(j,1)=A(j,2);\n",
+"    A(j,2)=A(j,3);\n",
+"    A(j,3)=C(j,1);\n",
+"end\n",
+"for j=1:3      //interchange of column 2 and 1\n",
+"    C(j,1)=A(j,2);\n",
+"    A(j,2)=A(j,1);\n",
+"    A(j,1)=C(j,1);\n",
+"end\n",
+"disp(A,'Inverse of Matrix A=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.4: Inverse_of_Triangular_Matrices.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.4\n",
+"//Inverse of Triangular Matrices\n",
+"//Page no. 260\n",
+"clc;clear;close;\n",
+"\n",
+"R=[2,4,-4,0;0,3,-3,-3;0,0,4,2;0,0,0,3];    //matrix R\n",
+"for i=4:-1:1\n",
+"    for j=4:-1:1\n",
+"        if(i>j)\n",
+"            Y(i,j)=0;\n",
+"        end\n",
+"        if(i==j)\n",
+"            Y(i,j)=1/R(i,j);\n",
+"        end\n",
+"        if(i<j)\n",
+"            l=0;\n",
+"            for k=i+1:j\n",
+"                l=l-R(i,k)*Y(k,j);\n",
+"            end\n",
+"            Y(i,j)=l/R(i,i);\n",
+"        end    \n",
+"    end\n",
+"end\n",
+"disp(Y,'Inverse of Matrix R=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.5: Inverse_of_Complex_Matrices.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.5\n",
+"//Inverse of Complex Matrices\n",
+"//Page no. 262\n",
+"clc;clear;close;\n",
+"\n",
+"A=[1,-1,0;2,3,4;0,1,2];\n",
+"B=[1,1,3;1,3,-3;-2,-4,-4];\n",
+"P=A+%i*B;\n",
+"disp(P,'Matrix P=')\n",
+"disp(A,'Matrix A=');disp(B,'Matrix B=');\n",
+"A1=inv(A);B1=inv(B);\n",
+"disp(A1,'Inverse of Matrix A=');\n",
+"disp(B1,'Inverse of Matrix B=');\n",
+"B1A=B1*A;disp(B1A,'Inverse(B)*A=');\n",
+"AB1A_B=A*B1A+B;disp(AB1A_B,'A*Inverse(B)*A+B=');\n",
+"AB1A_B1=inv(AB1A_B);disp(AB1A_B1,'Inverse(A*Inverse(B)*A+B)=');\n",
+"X=B1A*AB1A_B1;disp(X,'X=');\n",
+"Y=-1*AB1A_B1;disp(Y,'Y=');\n",
+"Q=X+%i*Y;disp(Q,'Inverse of Matrix P=')"
+   ]
+   }
+,
+{
+		   "cell_type": "markdown",
+		   "metadata": {},
+		   "source": [
+			"## Example 7.6: Iterative_Procedure.sce"
+		   ]
+		  },
+  {
+"cell_type": "code",
+	   "execution_count": null,
+	   "metadata": {
+	    "collapsed": true
+	   },
+	   "outputs": [],
+"source": [
+"//Example 7.6\n",
+"//Iterative Procedure\n",
+"//Page no. 265\n",
+"clc;clear;close;\n",
+"\n",
+"    A=[3,1,3/2;-5/4,-1/4,-3/4;-1/4,-1/4,-1/4];\n",
+"disp(A,'Matrix A=');\n",
+"B=[1,1,3.5;1,3,-3;-2,-3,-4];\n",
+"disp(B,'Assumed Matrix B=');\n",
+"e=0.1;\n",
+"\n",
+"//iterations\n",
+"E1=e;k=1;\n",
+"while(E1>=e)\n",
+"    printf('\n\n\nIteration %i\n',k)\n",
+"C=B*(2*eye(3,3)-A*B);disp(C,'Matrix C=');\n",
+"E=A*C-eye(3,3);disp(E,'Matrix E=');\n",
+"B=C;printf('\nInverse of Matrix A after %i iterations=',k);disp(B);\n",
+"E1=0;\n",
+"for i=1:3\n",
+"    for j=1:3\n",
+"        E1=E1+E(i,j)^2;\n",
+"    end\n",
+"end\n",
+"E1=sqrt(E1);\n",
+"k=k+1;\n",
+"end"
+   ]
+   }
+],
+"metadata": {
+		  "kernelspec": {
+		   "display_name": "Scilab",
+		   "language": "scilab",
+		   "name": "scilab"
+		  },
+		  "language_info": {
+		   "file_extension": ".sce",
+		   "help_links": [
+			{
+			 "text": "MetaKernel Magics",
+			 "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md"
+			}
+		   ],
+		   "mimetype": "text/x-octave",
+		   "name": "scilab",
+		   "version": "0.7.1"
+		  }
+		 },
+		 "nbformat": 4,
+		 "nbformat_minor": 0
+}