西安毛子科技大学三XIDIANUNIVERSITY解:A的特征多项式为0x-1-100=(x-1)3f(x)=| xE - A}=x-100x-1又A-E±0,(A-E)? = A?-2A+E(19-6396.9)00100:A的最小多项式为(x-1).解:A的特征多项式为 3 1 1 0 ( ) | | 0 1 0 ( 1) 0 0 1 x f x xE A x x x − − = − = − = − − 又 A E− 0, 2 2 ( ) 2 A E A A E − = − + 1 2 0 2 2 0 1 0 0 0 1 0 0 2 0 0 1 0 0 0 0 1 0 0 2 0 0 1 = − + = ∴ A的最小多项式为 2 ( 1) . x − 1 1 0 0 1 0 0 0 1 A =