//Example 3.2
//Gaussian Elimination Method
//Page no. 54
clc;clear;close;

A=[2,4,-6,-4;1,5,3,10;1,3,2,5];           //augmented matrix

//triangularization
for i=1:3
    for j=1:4
        if i==1 then
            B(i,j)=A(i,j)
        elseif i==2
            B(i,j)=A(i,j)-A(i,1)*A(i-1,j)/A(1,1)
            B(i+1,j)=A(i+1,j)-A(i+1,1)*A(i-1,j)/A(1,1)
        elseif i==3
            if j==1 then
                A=B
            end
            B(i,j)=B(i,j)-A(i,2)*B(i-1,j)/B(2,2)
        end
    end
end
disp(A,'Augmented Matrix=')
disp(B,'Triangulated Matrix=')
//back substitution
x(3)=B(3,4)/B(3,3);
printf('\nx(3)= %i\n',x(3))
for i=2:-1:1
    k=0
    for j=i+1:3
       k=k+B(i,j)*x(j)
    end
    x(i)=(1/B(i,i))*(B(i,4)-k)
     printf('\nx(%i)= %i\n',i,x(i))
end