Question

Find the values of the variables

Answer 1

Looks like you're given an equality between two matrices,

$\begin{bmatrix}-12&-w^2\\2f&3\end{bmatrix}=\begin{bmatrix}2k&-81\\-14&3\end{bmatrix}$

Two matrices are equal if the entries in the same positions (row and column) are equal. This means

$\begin{cases}-12=2k\\-w^2=-81\\2f=-14\\3=3\end{cases}$

We can ignore the last one, since it's clearly true. For the remaining, we get

$-12=2k\implies k=-\dfrac{12}2=-6$

$-w^2=-81\implies w^2=81\implies w=\pm9$

$2f=-14\implies f=-\dfrac{14}2=-7$