MATLAB program: Gaussian elimination without Pivoting
function x = Gauss(A, b)
% Solve linear system Ax = b
% using Gaussian elimination without pivoting
% A is an n by n matrix
% b is an n by k matrix (k copies of n-vectors)
% x is an n by k matrix (k copies of solution vectors)
[n, n] = size(A); % Find size of matrix A
[n, k] = size(b); % Find size of matrix b
x = zeros(n,k); % Initialize x
for i = 1:n-1
m = -A(i+1:n,i)/A(i,i); % multipliers
A(i+1:n,:) = A(i+1:n,:) + m*A(i,:);
b(i+1:n,:) = b(i+1:n,:) + m*b(i,:);
end;
% Use back substitution to find unknowns
x(n,:) = b(n,:)/A(n,n);
for i = n-1:-1:1
x(i,:) = (b(i,:) - A(i,i+1:n)*x(i+1:n,:))/A(i,i);
end