101 例3求020(k=1,2,L) 001 10 100 001 解:设C=020,A=020,B=000 00 00 000 则C=A+B,由于AB=BA,B2=O C=(A+B)=A+CLA B+CLAB+L +B 4+C4B 100 00/00 10k 02k0+k02k10000|=02k0 001 00 000)1001 0 1 0 2 0 ( 1,2, ) 0 0 3 1 . k k     =     例 求 L 2 1 1 2 2 2 1 1 1 1 0 1 1 0 0 0 0 1 0 2 0 0 2 0 0 0 0 0 0 1 0 0 1 0 0 0 O ( ) 1 0 0 1 0 0 0 0 1 0 2 0 0 2 0 0 0 0 0 0 1 0 0 1 0 0 0 k k k k k k k k k k k k k C C C k − − − −             = =       = + = =  = + = + + + + = +      = +             C A B C A B AB BA B C A B A A B A B B A A B L 解：设 = ， ， 则 ，由于 ， 1 0 0 2 0 0 0 1 k   k  =        