Question

6请解答图中计算题：请写出主要步骤

Answer 1

设A=

1 -1 -1 -1

-1 1 -1 -1

-1 -1 1 -1

-1 -1 -1 1

计算得

A^2 =

4 0 0 0

0 4 0 0

0 0 4 0

0 0 0 4

= 4E.

所以当n=2k时有

A^n = (A^2)^k = (4E)^k = 2^2k E

当n=2k+1时有

A^n = A(A^2)^k = 2^2k A