Question

Find the values of the variables

[-12 -w^2] = [2k -81]
[2f 3 ] [-14 3]

Please go step by step so I can understand. Thanks

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=-\frac{12}2=-6`

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

`2f=-14\implies f=-\frac{14}2=-7`