L =

   1   0   0
   2   1   0
   5  12   1

U =

   1   4   3
   0  -1   3
   0   0  -53

LU =

  1  4  3
  2  7  9
  5  8  -2

A =

  1  4  3
  2  7  9
  5  8  -2