Question

已知3阶矩阵A和3维列向量X满足A^3 *X=3AX-A^2*X,(^表示乘方 *表示乘法),且向量组X,AX,A^2*

Answer 1

AP = A(x,Ax,A^2x)

= (Ax,A^2x,A^3x)

= (Ax,A^2x,3Ax-A^2x)

= (x,Ax,A^2x)B

其中 B =

0 0 0

1 0 3

0 1 -2