Answer
See solution
Work Step by Step
\[
\begin{array}{c}
A=\left[\begin{array}{ccc}
3 & -1 & 2 \\
-3 & -2 & 10 \\
9 & -5 & 6
\end{array}\right] \sim\left[\begin{array}{ccc}
3 & -1 & 2 \\
0 & -3 & 12 \\
0 & -2 & 0
\end{array}\right] \sim\left[\begin{array}{ccc}
3 & -1 & 2 \\
0 & -3 & 12 \\
0 & 0 & -8
\end{array}\right]=U \\
{\left[\begin{array}{c}
4 \\
-3 \\
9
\end{array}\right]} & {\left[\begin{array}{c}
0 \\
-3 \\
-2
\end{array}\right]} & {\left[\begin{array}{c}
0 \\
0 \\
-8
\end{array}\right]^{\downarrow}}
\end{array}
\]
Dividing by 3,-3 and -8 respectively we can get the lower triangular Matrix
\[
L=\left[\begin{array}{ccc}
1 & 0 & 0 \\
-1 & 1 & 0 \\
3 & 2 / 3 & 1
\end{array}\right]
\]
