Answer
$T(x)=(-\frac{1}{2}x, \frac{5}{2}x,0,-x)$
Work Step by Step
We are given $T(2)=\begin{bmatrix}
-1 & 5 & 0 & 2
\end{bmatrix}$
Since $T(x)=\frac{x}{2}.T(2)\\
=\begin{bmatrix}
-1 & 5 & 0 & 2
\end{bmatrix}\frac{1}{2}\begin{bmatrix}
x
\end{bmatrix}\\
=(-\frac{1}{2}x, \frac{5}{2}x,0,-x)$
Hence, $T(x)=(-\frac{1}{2}x, \frac{5}{2}x,0,-x)$
