10)(A00)(010 解A=041 0元0+001 记为A+B 则可归纳得A=A+CAB+C2Ak-2B2+…+Bk (此处要用到数量矩阵A和任意同阶方阵可交换。) 且可直接得 B=001,B2=000,B3=000=O 000 000 000 所以A=A+CAB+C2A2B 1k-1 C22 k Cla k-11 1 2 2 2 2 3 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 C C . 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 , , 0 0 0 0 0 0 0 0 0 k k k k k k k A B A B B B B B B       − −             = = + =        =  +  +  + +              = = =            记为 解 ＋ 则可归纳得 (此处要用到数量矩阵 和任意同阶方阵可交换。) 且可直接得 1 1 2 2 2 1 1 2 2 1 1 . C C C C = . 0 C 0 0 k k k k k k k k k k k k k k k O A B B       − − − − − =  =  +  +        所以