11. Let $\varepsilon > 0$ be fixed. Show that there exists an integer $q \geqslant 1$ and an integer $n _ { 0 }$ such that for all $n \geqslant n _ { 0 }$,
$$\left\| V _ { n + q } \right\| _ { \infty } \leqslant ( \sigma ( A ) + \varepsilon ) ^ { q } \left\| V _ { n } \right\| _ { \infty }$$
where $A$ is the matrix from question 7.\\