An LU factorization is not unique. ONE such solution is the one that you came up with, probably due to an un-pivoted LU. The 25 in the (1,1) element of U suggests that you did no pivoting. For reasons of numerical computation, pivoting should always be used. If you computed an un-pivoted LU, then it will be less stable.
READ THE HELP FOR LU. READ THE HELP. ALWAYS.
help lu
[L,U] = lu(A) stores an upper triangular matrix in U and a
"psychologically lower triangular matrix" (i.e. a product of lower
triangular and permutation matrices) in L, so that A = L*U. A can be
rectangular.
The "psychologically lower triangular" result is due to the need for pivoting for stability.
For example, your code, which seems to lack pivoting, will fail to produce a viable result for a matrix like this:
A =[ 0 5 1
64 8 1
144 12 1];
which is indeed non-singular. But the built-in LU will have no problem.
