Answer
$a.\qquad\left[\begin{array}{l}
13\\
-7
\end{array}\right]$
$ b.\qquad$ not defined
Work Step by Step
If $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix
(so the number of columns of $A$ is the same as the number of rows of $B$),
then the matrix product $AB$ is the $m\times k$ matrix
whose $ij$-entry is the inner product of the $i\mathrm{t}\mathrm{h}$ row of $A$ and the jth column of $B.$
---
$a.$
$ABE=A(BE)$
$BE$ is defined ( a $2\times 3$ matrix multiplies a $3\times 1$ matrix)
$BE $ is a $2\times 1$ matrix.
$A(BE)$ is defined ( a $ 2\times$2 matrix multiplies a 2$\times 1$ matrix)
$A(BE) $ is a $2\times 1$ matrix.
$BE=\left[\begin{array}{l}
3(1)+\frac{1}{2}(2)+5(0)\\
1(1)+(-1)(2)+3(0)
\end{array}\right]=\left[\begin{array}{l}
4\\
-1
\end{array}\right]$
$ABE=A(BE)=\left[\begin{array}{l}
2(4)+(-5)(-1)\\
0(4)+(7)(-1)
\end{array}\right]=\left[\begin{array}{l}
13\\
-7
\end{array}\right]$
$b.$
$AHE=A(HE)$
$HE$ is not defined ( a $2\times 2$ matrix multiplies a $3\times 1$ matrix)
So, $AHE$ is not defined.
