Question

谁会矩阵?进来看下……设数列{an},{bn}满足a（n+1）=2an+3bn,b（n+1）=2bn,且【an+4】=M

Answer 1

(a(n+1),b(n+1))' = A (an,bn)' ( ' 是转置符号 )

则由已知得 A =

2 3

0 2

所以有

(a(n+4),b(n+4))' = A(a(n+3),b(n+3))'

= AA(a(n+2),b(n+2))'

= AAA(a(n+1),b(n+1))'

= AAAA(an,bn)'

即 M = A^4.

A^2 =

4 12

0 4

所以 M= A^4 = (A^2)^2 =

16 96

0 16

OK了!