Solution
= Solution
<Gaussian elimination> gives the <LU decomposition>
$$
\boxed{
L=\begin{pmatrix}
1&0&0&0\\
0&2&0&0\\
0&5&2&0\\
3&-4&3&1
\end{pmatrix},
\qquad
U=\begin{pmatrix}
1&1&0&3\\
0&1&1&6\\
0&0&1&1\\
0&0&0&2
\end{pmatrix}}.
$$
The prescribed diagonal entries of $L$ are visible, and direct multiplication gives $LU=A$.