## Matrix Operations with Transpose

## Problem 636

Calculate the following expressions, using the following matrices:

\[A = \begin{bmatrix} 2 & 3 \\ -5 & 1 \end{bmatrix}, \qquad B = \begin{bmatrix} 0 & -1 \\ 1 & -1 \end{bmatrix}, \qquad \mathbf{v} = \begin{bmatrix} 2 \\ -4 \end{bmatrix}\]

**(a)** $A B^\trans + \mathbf{v} \mathbf{v}^\trans$.

**(b)** $A \mathbf{v} – 2 \mathbf{v}$.

**(c)** $\mathbf{v}^{\trans} B$.

**(d)** $\mathbf{v}^\trans \mathbf{v} + \mathbf{v}^\trans B A^\trans \mathbf{v}$.