A sequence is defined by $a_n = a_{n-1} + 2a_{n-2}$ with $a_0 = 1, a_1 = 1$. This can be written as $\begin{pmatrix} a_n \\ a_{n-1} \end{pmatrix} = M^{n-1} \begin{pmatrix} a_1 \\ a_0 \end{pmatrix}$ for $n \geq 2$. What is the matrix $M$?