why i am not getting the exact answer when i use lu built in function?

A=[25 5 1;64 8 1;144 12 1];
C=[106.8;177.2;279.2];
[L,U] = lu(A)
L =

    0.1736    1.0000         0
    0.4444    0.9143    1.0000
    1.0000         0         0
U =

144.0000   12.0000    1.0000
       0    2.9167    0.8264
       0         0   -0.2000

and the manual solution is

L=
1    0   0
2.56 1   0
5.76 3.5 1
U=
25 5    1
0 -4.8 -1.56
0  0    0.7

Answer 1

[John D'Errico]

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.

[Eliza]

yes ,you are right .I intentionally solve it as un-pivoting LU .Could I solve it also by MATLAB by using LU without pivoting ? because I wanna solve it for this matrix only as checking of my manually solution .