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+//Example 3.10

+//Triangularization Method

+//Page no. 62

+clc;clear;close;

+

+A=[2,4,-6;1,5,3;1,3,2];

+B=[-4;10;5];

+printf('A can be factorizaed as follows:\n')

+printf('\tL\t\t  *\t\tU\t\t  =\t\tA')

+U(2,1)=0;U(3,1)=0;U(3,2)=0;

+L(1,2)=0;L(1,3)=0;L(2,3)=0;

+for i=1:3

+    L(i,i)=1

+end

+for i=1:3

+    U(1,i)=A(1,i)

+end

+L(2,1)=1/U(1,1);

+for i=2:3

+    U(2,i)=A(2,i)-U(1,i)*L(2,1);

+end

+L(3,1)=1/U(1,1);

+L(3,2)=(A(3,2)-U(1,2)*L(3,1))/U(2,2);

+U(3,3)=A(3,3)-U(1,3)*L(3,1)-U(2,3)*L(3,2);

+printf('\n')

+for i=1:3

+    for j=1:3

+        printf('%.2f\t',L(i,j))

+    end

+    

+    if(i==2)

+        printf('  *     ')

+    else

+        printf('\t')

+    end

+    

+    for j=1:3

+        printf('%.2f\t',U(i,j))

+    end

+    if(i==2)

+        printf('  =     ')

+    else

+        printf('\t')

+    end

+    for j=1:3

+        printf('%.2f\t',A(i,j))

+    end

+    printf('\n')

+end

+printf('\nY=U*X')

+    Y=inv(L)*B

+    X=inv(U)*Y

+printf('\n\nX=')

+for i=1:3

+    printf('\n   %i',X(i,1))

+end
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