Question

已知三阶矩阵A及3维列向量X,使向量组X,AX,A^3X线性无关,且满足A^3X=3AX-2A^2X,记B=（X,AX,

Answer 1

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

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

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

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

= BC

其中 C =

0 0 0

1 0 3

0 1 -2