Let $P$ be a $2 \times 3$ matrix, $Q$ an $m \times 5$ matrix, and $R$ a $p \times q$ matrix. Find the values of $m$, $p$, and $q$ such that the operation $Q - PR$ is possible.
So I figured that $p = 3$.
Is $m=2$ and $q=5$?
Just need to make sure I'm on the right track.
Thanks for any help in advance.
When you multiply matrices, the inner dimensions have to match, and the result has the outer dimensions.
Here, we are multiplying $P$, which is $\color{red}{2} \times \color{blue}{3}$, with $R$, which is $\color{blue}{p} \times \color{red}{q}$.
In order to multiply the two matrices, we must have $\color{blue}{3} = \color{blue}{p}$, and the result $PR$ will have dimenions $\color{red}{2} \times \color{red}{q}$. Since we are adding the matrix $PR$ with $Q$, which is $m \times 5$, their dimensions must match, which means we must have $m = 2$ and $q = 5$.
So yes, you were on the right track.