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.)

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: \(\mathbf{u}+\mathbf{v}=\boxed{[-11, 10]}\)