Answer
\begin{align*}
U+V&=(0,8)\\
U-V&=(-8,0)\\
2U-3V&=(-20,-4).
\end{align*}
Work Step by Step
We have $U=\langle -4,4\rangle, V=\langle 4,4\rangle.$
First find $U+V$,
\begin{align*}
U+V=(-4,4)+(4,4)\\
&=(-4+4,4+4)\\
&=(0,8).
\end{align*}
Hence, $U+V=(0,8).$
Then find $U-V$,
\begin{align*}
U-V&=(-4,4)-(4,4)\\
&=(\left(-4\right)-4,4-4)\\
&=(-8,0).
\end{align*}
Hence, $U-V=(-8,0).$\\
In the end find,
\begin{align*}
2U-3V&=2(-4,4)-3(4,4)\\
&=(-8,8)-(12,12)\\
&=\begin{pmatrix}\left(-8\right)-12,8-12\end{pmatrix}\\
&=(-20,-4).
\end{align*}
