Answer
$a=2$
$ z=-3$
$m=8$
$k=1$
Work Step by Step
Two matrices are equal if they have the same dimension and
if corresponding elements, position by position, are equal.
---
Adding the two matrices on the LHS,
$\left[\begin{array}{lll}
4a+2 & 5z+1 & 10m\\
10k & 5 & 9
\end{array}\right]=\left[\begin{array}{lll}
10 & -14 & 80\\
10 & 5 & 9
\end{array}\right]$
The dimensions are both 2$\times$3, so we equate, position by position
$4a+2=10 \quad \Rightarrow \quad 4a= 8 \quad \Rightarrow \quad a=2$
$5z+1=-14 \quad \Rightarrow \quad 5z=-15 \quad \Rightarrow \quad z=-3$
$10m=80 \quad \Rightarrow \quad m=8$
$10k=10 \quad \Rightarrow \quad k=1$
