Matrices & Systems · Hard problem

A linear transformation, represented by the $2\times2$ matrix $M$, sends $\begin{pmatrix}1\\2\end{pmatrix}$ to $\begin{pmatrix}5\\4\end{pmatrix}$ and sends $\begin{pmatrix}2\\1\end{pmatrix}$ to $\begin{pmatrix}7\\8\end{pmatrix}$. Find the sum of all four entries of $M$.