已知数列 $\left\{x_n\right\} .\left\{y_n\right\} .\left\{z_n\right\}$ 满足 $x_0=-1, y_0=0, z_0=2$. 且 $\left\{\begin{array}{c}x_n=-2 x_{n-1}+2 z_{n-1} \\ y_n=-2 y_{n-1}-2 z_{n-1} \\ z_n=-6 x_{n-1}-3 y_{n-1}+3 z_{n-1}\end{array}\right.$,记 $\alpha_n=\left\{\begin{array}{l}x_n \\ y_n \\ z_n\end{array}\right\}$, 写出海足 $\alpha_n=A \alpha_{n-1}$ 的矩阵 $A$, 并求 $A^n$ 及 $x_n, y_n, z_n(n=1,2, \cdots)$.