这个矩阵的n次幂怎么求?A= 1 -√3√3 1 求这个矩阵的n次幂

网友回答

A^2 =-2 -2√3
2√3 2A^3 = AA^2 =
-8 00 -8= -8E.所以 当n = 3k 时,A^n = (A^3)^k = (-8E)^k = (-8)^kE
当n = 3k+1 时,A^n = A(A^3)^k = A(-8E)^k = (-8)^kA
当n = 3k+2 时,A^n = A^2(A^3)^k = A^2(-8E)^k = (-8)^kA^2 = (-8)^k *
-2 -2√3
2√3 2======以下答案可供参考======
供参考答案1:
1 ，(-1)^n*3^(n/2)
3^(n/2),1