Chapter A.1, Problem 1P

Given the matrices

$\text{A}=\left(\begin{array}{cc}2& 2\\ -1& 3\end{array}\right),\text{B}=\left(\begin{array}{ccc}-1& 1& -2\\ 1& 3& 4\end{array}\right),\text{x}=\left(\begin{array}{c}2\\ 3\end{array}\right),\text{y}=\left(\begin{array}{ccc}1& 2& -1\end{array}\right)$

Compute each of the following for which the indicated operations are defined:

$\begin{array}{lllllll}\text{(a)}\text{4A}\hfill & \hfill & \hfill & \text{(b)}\text{-2x}\hfill & \hfill & \hfill & \text{(c)}\text{A}\text{+}\text{B}\hfill \\ \text{(d)}\text{Ax}\hfill & \hfill & \hfill & \text{(e)}\text{Bx}\hfill & \hfill & \hfill & \text{(f)}\text{AB}\hfill \\ \text{(g)}\text{BA}\hfill & \hfill & \hfill & \text{(h)}{\text{B}}^{\text{T}}\text{A}\hfill & \hfill & \hfill & \text{(i)}\text{yB}\hfill \\ \text{(j)}{\left(\text{AB}\right)}^{\text{T}}\hfill & \hfill & \hfill & \text{(k)}{\text{x}}^{\text{T}}\text{Ax}\hfill & \hfill & \hfill & \text{(l)}{\text{xBy}}^{\text{T}}\hfill \end{array}$