Answer
\[\mathbf{u}+\mathbf{v}=\left\langle {{u}_{1}}+{{v}_{1}},{{u}_{2}}+{{v}_{2}} \right\rangle \]
Work Step by Step
\[\begin{align}
& \text{If }\mathbf{u}=\left\langle {{u}_{1}},{{u}_{2}} \right\rangle \text{ and }\mathbf{v}=\left\langle {{v}_{1}},{{v}_{2}} \right\rangle ,\text{ then} \\
& \mathbf{u}+\mathbf{v}=\left\langle {{u}_{1}},{{u}_{2}} \right\rangle +\left\langle {{v}_{1}},{{v}_{2}} \right\rangle \\
& \mathbf{u}+\mathbf{v}=\left\langle {{u}_{1}}+{{v}_{1}},{{u}_{2}}+{{v}_{2}} \right\rangle \\
\end{align}\]
