clear ;

rand('seed', 1234); % Initialize uniform random number generator

n = 200; % Matrix dimension

A = rand(n,n); % Create random matrix
xsol = rand(n,1);
b = A*xsol;

for k=1:n-1
  for i=k+1:n
    A(i,k) = A(i,k)/A(k,k);
    A(i,k+1:n) = A(i,k+1:n) - A(i,k)*A(k,k+1:n);
  end
end

% Verifications

U = triu(A); % Extract the upper triangular factor
L = tril(A); % Extract lower triangular part
D = diag(diag(A)); % Create diagonal matrix
L = L - D + eye(n); % Construct the actual lower triangular factor

%Solving the system
y = L \ b;
x = U \ y;
norm(x - xsol)/norm(xsol)