Answer
See solution
Work Step by Step
\[
\begin{array}{l}
A=\left[\begin{array}{cccc}
1 & 4 & -1 & 5 \\
3 & 7 & -2 & 9 \\
-2 & -3 & 1 & -4 \\
-1 & 6 & -1 & 7
\end{array}\right] \sim\left[\begin{array}{cccc}
1 & 4 & -1 & 5 \\
0 & -5 & 1 & -6 \\
0 & 5 & -1 & 6 \\
0 & 10 & -2 & 12
\end{array}\right] \sim\left[\begin{array}{cccc}
1 & 4 & -1 & 5 \\
0 & -5 & 1 & -6 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{array}\right]=U \\
{\left[\begin{array}{c}
1 \\
3 \\
-2 \\
-1
\end{array}\right]} & {\left[\begin{array}{c}
-5 \\
5 \\
10
\end{array}\right]}
\end{array}
\]
Dividing by 1 and $-5,$ we can get the lower triangular Matrix
\[
\begin{array}{l}
L=\left[\begin{array}{cccc}
1 & 0 & 0 & 0 \\
3 & 1 & 0 & 0 \\
-2 & -1 & 1 & 0 \\
-1 & -2 & 0 & 1
\end{array}\right] \\
U=\left[\begin{array}{cccc}
1 & 4 & -1 & 5 \\
0 & -5 & 1 & -6 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{array}\right]
\end{array}
\]
