LU Decomposition Trouble

Question

I'm having trouble decomposing a given matrix, A into its unit lower triangular matrix, L and upper triangular matrix, U.

After watching this, Prof. Kaw's video on the topic, my answer isn't making sense when I seek to return to by original matrix by [L] X [U]. (I checked this with MATLAB).

The matrix:

 9     7     1
 63    51     2
-63   -53     8

What I get:

U =

 9   7     1
 0   2    -5
 0   0    25

L =

 1     0     0
 7     1     0
 7     2     1

But this doesn't work, why?

Answer 1

Your $L$ should be $$ \begin {bmatrix}1&0&0\\7&1&0\\-7&-2&1\end {bmatrix}$$

and your $U$ should be $$ \begin {bmatrix}9&7&1\\0&2&-5\\0&0&5\end {bmatrix}$$