Compute $\mathbf{u}+\mathbf{v}$ and $\mathbf{u}-\mathbf{2} \mathbf{v}$.
\[
u=\left[\begin{array}{r}
-6 \\
4
\end{array}\right], v=\left[\begin{array}{r}
-5 \\
6
\end{array}\right]
\]
$\mathbf{u}+\mathbf{v}=\square$ (Simplify your answer.)
Answer
Final Answer: \(\mathbf{u}+\mathbf{v}=\boxed{[-11, 10]}\)
Step 1 ：The question is asking for the sum of two vectors, \(\mathbf{u}\) and \(\mathbf{v}\). To add two vectors, we simply add their corresponding components. In this case, we add the first component of \(\mathbf{u}\) to the first component of \(\mathbf{v}\), and the second component of \(\mathbf{u}\) to the second component of \(\mathbf{v}\).
Step 2 ：\(\mathbf{u} = [-6, 4]\)
Step 3 ：\(\mathbf{v} = [-5, 6]\)
Step 4 ：Adding the corresponding components of \(\mathbf{u}\) and \(\mathbf{v}\), we get \(\mathbf{u} + \mathbf{v} = [-11, 10]\)
Step 5 ：Final Answer: \(\mathbf{u}+\mathbf{v}=\boxed{[-11, 10]}\)
