Suppose that $\ltdefn{T}{U}{V}$ and $\ltdefn{S}{V}{W}$ are linear transformations, and that $B$, $C$ and $D$ are bases for $U$, $V$, and $W$. Using only Definition MR define matrix representations for $T$ and $S$. Using these two definitions, and Definition MR, derive a matrix representation for the composition $\compose{S}{T}$ in terms of the entries of the matrices $\matrixrep{T}{B}{C}$ and $\matrixrep{S}{C}{D}$. Explain how you would use this result to motivate a definition for matrix multiplication that is strikingly similar to Theorem EMP.