设 $A =\left[\begin{array}{ccc}1 & -2 & 3 \\ -1 & 2 & -3 \\ 1 & 4 & -3\end{array}\right], \xi_1=\left[\begin{array}{c}1 \\ -1 \\ -1\end{array}\right]$, 求满足 $A \xi_2=2 \xi_1, A ^2 \xi_3=6 \xi_1$ 的所有向量 $\xi_2, \xi_3$.
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