Question

Find two matrices A and B such that 2A-3B= [5 0
-1 2]

(5 & 0 are on top; -1 & 2 are on the bottom— it’s a 2x2 matrix)

Answer 1

The easy answer: If, say, B is the zero matrix, i.e.

$B=\begin{bmatrix}0&0\\0&0\end{bmatrix}$

then

$2A=\begin{bmatrix}5&0\\-1&2\end{bmatrix}\implies A=\begin{bmatrix}\dfrac52&0\\\\-\dfrac12&1\end{bmatrix}$