Answer
See solution
Work Step by Step
\[
T(\mathbf{x})=\left[\begin{array}{c}
x_{1}-2 x_{2} \\
-x_{1}+3 x_{2} \\
3 x_{1}-2 x_{2}
\end{array}\right]=A\left[\begin{array}{c}
x_{1} \\
x_{2}
\end{array}\right]=\left[\begin{array}{cc}
1 & -2 \\
-1 & 3 \\
3 & -2
\end{array}\right]\left[\begin{array}{l}
x \\
x
\end{array}\right]
\]
So
\[
T(\mathbf{x})=\left[\begin{array}{c}
-1 \\
4 \\
9
\end{array}\right]
\]
row decrease the augmented matrix:
\[
\left[\begin{array}{ccc}
1 & -2 & -1 \\
-1 & 3 & 4 \\
3 & -2 & 9
\end{array}\right]
\]
Augmented Matrix
\[
\left.\begin{array}{ccc}
1 & -2 & -1 \\
0 & 1 & 3 \\
0 & 4 & 12
\end{array}\right]
\]
$\left[\begin{array}{lll}1 & 0 & 5 \\ 0 & 1 & 3 \\ 0 & 0 & 0\end{array}\right]$
$R_{1}=R_{1}+2 R_{2}$
$\mathbf{x}=\left[\begin{array}{l}5 \\ 3\end{array}\right]$
