Suppose $a = \begin{pmatrix} a_1 & \dots & a_n \end{pmatrix}$ is a $1$-by-$n$ matrix and $C$ is an $n$-by-$p$ matrix. Prove that

In other words, show that $aC$ is a linear combination of the rows of $C$, with the scalars that multiply the rows coming from $a$.

TODO