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1. Scaling matrix powers to converge ●●●○○ 50 ptsLet $A=\begin{pmatrix}1&-1&0\\-1&2&-1\\0&-1&1\end{pmatrix}$. Find the real number $a$ for which the limit $\lim_{n\to\infty} a^nA^n$ exists and is non-zero, where a sequence of matrices $B_n$ converges to $B$ when $B_nx\to Bx$ for every $x\in\mathbb{R}^3$. Give $a$ rounded to two decimal places.