Consider the system of coupled recurrences: $a_n = 2b_{n-1}$ and $b_n = a_{n-1} + 2b_{n-1}$. This can be written in matrix form as $\begin{pmatrix} a_n \\ b_n \end{pmatrix} = M \begin{pmatrix} a_{n-1} \\ b_{n-1} \end{pmatrix}$. What is the matrix $M$?