Answer
See solution
Work Step by Step
\[
T(\mathbf{x})=\left[\begin{array}{c}
2 x_{2}-3 x_{1} \\
x_{1}-4 x_{2} \\
0 \\
x_{2}
\end{array}\right]=A\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}\right]
\]
To express $T(x)$ as $A x,$ write $T(x)$ and $x$ as column vectors, and then fill in the entries in $A$ by inspection
\[
T(\mathbf{x})=\left[\begin{array}{cc}
-3 & 2 \\
1 & -4 \\
0 & 0 \\
0 & 1
\end{array}\right]\left[\begin{array}{l}
x_{1} \\
x_{2}
\end{array}\right]
\]
since $x$ has 2 entries, $A$ has 2 columns. So $T(x)$ has 4 entries, $A$ has 4 rows
