Answer
\begin{align*}
U+V&=(-1,9)\\
U-V&=(3,-1)\\
2U-3V&=(8,-7).
\end{align*}
Work Step by Step
We have $U=\langle 1,4\rangle, V=\langle -2,5\rangle.$
First find $U+V$,
\begin{align*}
U+V&=(1,4)+(-2,5)\\
&=(1+(-2),4+5)\\
&=(-1,9).
\end{align*}
Hence, $U+V=(-1,9).$
Then find $U-V$,
\begin{align*}
U-V&=(1,4)-(-2,5)\\
&=(1-(-2),4-5)\\
&=(3,-1).
\end{align*}
Hence, $U-V=(3,-1).$
In the end find,
\begin{align*}
2U-3V&=2(1,4)-3(-2,5)\\
&=(2,8)-(-6,15)\\
&=(2-(-6),8-15)\\
&=(8,-7).
\end{align*}
