% Input: A - nxn matrix and n- its dimension
%Output: LU factorization of A.
function[L,U]=factornaive(A,n)
L=eye(n,n);
for j=1:n-1
    for k=j+1:n
  L(k,j)=A(k,j)/A(j,j);
  for s=j:n
      A(k,s)=A(k,s)-L(k,j)*A(j,s);
  end
    end
end
U=A;
___________________________________________________________________________
A=[1 2 1; 2 2 3; -1 -3 0]

A =

     1     2     1
     2     2     3
    -1    -3     0
    
[L U]=factornaive(A,3)

L =

    1.0000         0         0
    2.0000    1.0000         0
   -1.0000    0.5000    1.0000


U =

    1.0000    2.0000    1.0000
         0   -2.0000    1.0000
         0         0    0.5000