求向量组a1=(1,2,3,4)a2=(2,3,4,5)a3=(3,4,5,6)a4=(4,5,6,7)的秩和极大线性无关组.
问题描述:
求向量组a1=(1,2,3,4)a2=(2,3,4,5)a3=(3,4,5,6)a4=(4,5,6,7)的秩和极大线性无关组.
原题有t次方,a1=(1,2,3,4)^t,a2=(2,3,4,5)^t,a3=(3,4,5,6)^t,a4=(4,5,6,7)^t
答
(a1,a2,a3,a4) =
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 7
r4-r3,r3-r2,r2-r1
1 2 3 4
1 1 1 1
1 1 1 1
1 1 1 1
r1-r2,r3-r3,r4-r2
0 1 2 3
1 1 1 1
0 0 0 0
0 0 0 0
所以向量组的秩为2,a1,a2 是一个极大无关组.