$\displaystyle x_{xn-1}= 5_{xn-1} - 6_{xn-2}; for\ n\geq2\ x_{1} = 1\ x_{0} = 0 $

prove by induction that:

$\displaystyle \begin{bmatrix}x_{n}\\ x_{n-1} \end{bmatrix} = \begin{bmatrix}\5 &-6 \\ 1 & 0\end{bmatrix}^{n-1}\begin{bmatrix}\1\\0 \end{bmatrix} $