Answer
\begin{align*}
U+V&=7i+7j.\\
U-V&=-3i+3j.\\
3U+2V&=16i+19j.
\end{align*}
Work Step by Step
We have $U=2i+5j, V=5i+2j.$
First find $U+V$,
\begin{align*}
U+V&=(2i+5j)+(5i+2j)\\
&=2i+5i+5j+2j\\
&=7i+7j.
\end{align*}
Hence, $U+V=7i+7j.$
Then find $U-V$,
\begin{align*}
U-V&=(2i+5j)-(5i+2j)\\
&=2i-5i+5j-2j\\
&=-3i+3j.
\end{align*}
Hence, $U-V=-3i+3j.$
In the end find,
\begin{align*}
3U+2V&=3(2i+5j)+2(5i+2j)\\
&=6i+15j+10i+4j\\
&=16i+19j.
\end{align*}
