Question

Given that $P = \begin{bmatrix} 2 & -1 \\ 3 & 4 \end{bmatrix}$, $Q = \begin{bmatrix} 5 & 2 \\ 7 & 4 \end{bmatrix}$ and $R = \begin{bmatrix} 2 & 5 \\ 3 & 8 \end{bmatrix}$, find a matrix $S$ such that $PQ - RS$ is a null matrix.

Hint:

Since $|R| = 1$, finding the inverse requires no fractional scaling. When solving equations of the form $RS = B$, make sure to pre-multiply by $R^{-1}$ on the left hand side, because matrix multiplication is generally non-commutative ($R^{-1}B \neq BR^{-1}$).

Answer 1