Answer
$\begin{bmatrix}6\\3\end{bmatrix}$, $\begin{bmatrix}-2\\6\end{bmatrix}$, $\begin{bmatrix}4\\9\end{bmatrix}$
Work Step by Step
Since $T$ is a linear transformation, it must be that $T(a\vec{x}+b\vec{y})=aT(\vec{x})+bT(\vec{y})$ for any vectors $\vec{x}$, $\vec{y}$ in the domain and for any scalars $a$, $b$. Hence:
$T(3\vec{u})=3T(\vec{u})=3\begin{bmatrix}2\\1\end{bmatrix}=\begin{bmatrix}6\\3\end{bmatrix}$
$T(2\vec{v})=2T(\vec{v})=2\begin{bmatrix}-1\\3\end{bmatrix}=\begin{bmatrix}-2\\6\end{bmatrix}$
$T(3\vec{u}+2\vec{v})=3T(\vec{u})+2T(\vec{v})=\begin{bmatrix}6\\3\end{bmatrix}+\begin{bmatrix}-2\\6\end{bmatrix}=\begin{bmatrix}4\\9\end{bmatrix}$
