Question

已知矩阵A 求 A^4=?已知矩阵A= 1 1 -1-1 -1 11 1 -1 求 A^4 （就是A的4次幂）

Answer 1

设

b =

1

-1

1

c = (1,1,-1),

则A = bc,A^4 = (bc)(bc)(bc)(bc) = b(cb)(cb)(cb)c = b(cb)^3c.

而cb = -1,故A^4 = b(-1)^3c = -bc = -A =

-1 -1 1

1 1 -1

-1 -1 1