Answer
\begin{align*}
U+V&=(2,-7)\\
U-V&=(2,7)\\
2U-3V&=(4,21).
\end{align*}
Work Step by Step
We have $U=\langle 2,0\rangle, V=\langle 0,-7\rangle.$
First find $U+V$,
\begin{align*}
U+V&=(2,0)+(0,-7)\\
&=(2+0,0-7)\\
&=(2,-7).
\end{align*}
Hence, $U+V=(2,-7).$
Then find $U-V$,
\begin{align*}
U-V&=(2,0)-(0,-7)\\
&=(2-0,0-(-7))\\
&=(2,7).
\end{align*}
Hence, $U-V=(2,7).$
In the end find,
\begin{align*}
2U-3V&=2(2,0)-3(0,-7)\\
&=(4,0)-(0,-21)\\
&=(4-0,0+21)\\
&=(4,21).
\end{align*}