Answer
\begin{align*}
U+V&=(-1,3)\\
U-V&=(9,-1)\\
2U-3V&=(23,-4).
\end{align*}
Work Step by Step
We have $U=\langle 4,1\rangle, V=\langle -5,2\rangle.$
First find $U+V$,
\begin{align*}
U+V&=(4,1)+(-5,2)\\
&=(4+(-5),1+2)\\
&=(-1,3).
\end{align*}
Hence, $U+V=(-1,3).$
Then find $U-V$,
\begin{align*}
U-V&=(4,1)-(-5,2)\\
&=(4-(-5),1-2)\\
&=(9,-1).
\end{align*}
Hence, $U-V=(9,-1).$
In the end find,
\begin{align*}
2U-3V&=2(4,1)-3(-5,2)\\
&=(8,2)-(-15,6)\\
&=(8-(-15),2-6)\\
&=(23,-4).
\end{align*}
