P is a 2 times 2 matrix.Determine p if
Have you even tried to do this yourself? It's very straight forward.
$\displaystyle 3\begin{bmatrix}1 & 0 \\ 2 & 4\end{bmatrix}- 2P= \begin{bmatrix}-2 & -3 \\ 4 & -5\end{bmatrix]$.
Since P must be a 2x2 matrix in order to be able to subtract 2P, write it as [tex]\begin{bmatrix}a & b \\ c & d\end{bmatrix}:
$\displaystyle 3\begin{bmatrix}1 & 0 \\ 2 & 4\end{bmatrix}- 2\begin{bmatrix}a & b \\ c & d\end= \begin{bmatrix}-2 & -3 \\ 4 & -5\end{bmatrix]$.
Do the indicated calculations and you will have 4 separate linear equations for a, b, c, and d. For example, one equation is 1- 2a= -2. That's easy to solve.
let $\displaystyle \begin{bmatrix}
1 & 0\\
2 & 4
\end{bmatrix} $ be A
and let
$\displaystyle \begin{bmatrix}
-2 & -3\\
4 & -5
\end{bmatrix} $ be C.
So we have $\displaystyle 3A-2P=C$
to find P, rearange it
$\displaystyle -P=\frac{C-3A}{2}$
$\displaystyle P=-\frac{C-3A}{2}$
Can you do it now?