Answer
$a.\qquad\left[\begin{array}{lll}
5 & -3 & 10\\
6 & 1 & 0\\
-5 & 2 & 2
\end{array}\right]$
$b.\qquad\left[\begin{array}{l}
-1\\
8\\
-1
\end{array}\right]$
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 $B.$
---
$a.$
$GF$ is defined and is a 3$\times$3 matrix
$GF=\left[\begin{array}{lll}
5+0+0 & 0+(-3)+0 & 0+0+10\\
6+0+0 & 0+1+0 & 0+0+0\\
-5+0+0 & 0+2+0 & 0+2+0
\end{array}\right]$
$=\left[\begin{array}{lll}
5 & -3 & 10\\
6 & 1 & 0\\
-5 & 2 & 2
\end{array}\right]$
$b.$
$GE$ is defined and is a 3$\times$1 matrix.
$GE=\left[\begin{array}{l}
5(1)+(-3)(2)+ 10(0)\\
6(1)+1(2)+ 0(0)\\
-5(1)+2(2)+ 2(0)
\end{array}\right]=\left[\begin{array}{l}
-1\\
8\\
-1
\end{array}\right]$
