Hi Usman, the following code works for me. I first converted into upper triangular and did backward sub.
A = [3 2 1;-4 5 7;1 0 -9];
B = [1;4;5];
[m,n] = size(A);
x = zeros(m,1);
for i = 1:m-1
factor = A(i+1:m,i)/A(i,i);
% i = 1 => factors = A(2,1)/A(1,1) & A(3,1)/A(1,1) short note % A(2:3,1)/A(1,1)
A(i+1:m,:) = A(i+1:m,:) - factor*A(i,:);
% making non-diagonal elements zero
% in this case -4 = -4 - (-4/3)*3
% for first iteration A(2,1) AND A(3,1) become zero
% second iteration A(3,2) becomes zero
B(i+1:m,:) = B(i+1:m,:) - factor*B(i,:);
end
% now we have upper triangular matrix
% so z value = b(3)/a(3,3)
% and keep doing backward sub
x(m,:) = B(m,:)/A(m,m);
for i = m-1:-1:1
x(i,:) = (B(i,:) - A(i,i+1:m)*x(i+1:m,:))/A(i,i);
end
x
