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//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
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