设矩阵A=0100001000010000,则A3的秩为_.

问题描述:

设矩阵A=

0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0
,则A3的秩为______.

由于A=

0 1 0 0
0 0 1 0
0 0 0 1
0 0 0 0

则A3=
0
0
0
0
0
0
0
0
0
1
0
0
0 0 0 0

所以r(A)=1
故答案为:1.