rref - computes matrix row echelon form by lu transformations
rref computes the row echelon form of the given matrix by left lu decomposition. If ones need the transformation used just call X=rref([A,eye(m,m)]) the row echelon form R is X(:,1:n) and the left transformation L is given by X(:,n+1:n+m) such as L*A=R
A=[1 2;3 4;5 6]; X=rref([A,eye(3,3)]); R=X(:,1:2) L=X(:,3:5);L*A