Answer
$U+V=(8,0).$
$U-V=(0,8).$
$2U-3V=(4,-20).$
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)\\
&=(8,0).
\end{align*}
Hence, $U+V=(8,0).$
Then find $U-V$,
\begin{align*}
U-V&=(4,4)-(4,-4)\\
&=(4-4,4-(-4))\\
&=(0,8).
\end{align*}
Hence, $U-V=(0,8).$\\
In the end find,
\begin{align*}
2U-3V=2(4,4)-3(4,-4)\\
&=(8,8)-(12,-12)
&=(8-12,8-(-12))\\
&=(4,-20).
\end{align*}
Hence, $2U-3V=(4,-20).$
