数学试题讲解

设

A = [\begin{array}{lll} 1 & 2 & 2 \\ 2 & 1 & 2 \\ 2 & 2 & 1 \end{array}], B = [\begin{array}{lll} - 3 & 2 & 3 \\ - 1 & 1 & 1 \\ - 4 & 1 & 4 \end{array}]

求矩阵

A, B

的全部特征值及对应的特征向量．