数学试题讲解

设

A = [\begin{array}{ccc} 1 & - 2 & 3 \\ - 1 & 2 & - 3 \\ 1 & 4 & - 3 \end{array}], ξ_{1} = [\begin{matrix} 1 \\ - 1 \\ - 1 \end{matrix}]

, 求满足

A ξ_{2} = 2 ξ_{1}, A^{2} ξ_{3} = 6 ξ_{1}

的所有向量

ξ_{2}, ξ_{3}