Answer
a.
$u+v\in V$
b. Sample: let $u=\left[\begin{array}{l}
1\\
1
\end{array}\right], c=-1.$
Work Step by Step
a.
If $\mathrm{u}=\left[\begin{array}{l}
u_{1}\\
u_{2}
\end{array}\right]\in V,$ and $\mathrm{v}=\left[\begin{array}{l}
v_{1}\\
v_{2}
\end{array}\right] \in V$,
means that $u_{1},u_{2},v_{1},v_{2} \geq 0.$
The sum of nonnegative numbers is nonnegative,
$u_{1}+v_{1} \geq 0, \quad u_{2}+v_{2} \geq 0$
$\Rightarrow u+v=\left[\begin{array}{l}
u_{1}+v_{1}\\
u_{2}+v_{2}
\end{array}\right]\in V.$
b.
Sample: let $u=\left[\begin{array}{l}
1\\
1
\end{array}\right],\quad c=-1.$
$u\in V,$ but $ cu=\left[\begin{array}{l}
-1\\
-1
\end{array}\right]\not\in V$
