5. (18%) Compute L and U for the following matrix A:

$$A = \begin{bmatrix} 4 & 4 & 4 & 4 \\ 4 & 5 & 5 & 5 \\ 4 & 5 & 6 & 6 \\ 4 & 5 & 6 & 7 \end{bmatrix}$$