求向量组（I）的秩,求向量组a1=(1,2,-1,3),a2=(2,3,-3,4),a4=(4,7,-6,7),a4=(

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/14 07:03:29

求向量组（I）的秩,
求向量组a1=(1,2,-1,3),a2=(2,3,-3,4),a4=(4,7,-6,7),a4=(3,5,-4,7)的秩,并求出它的一个极大无关组.

1 2 4 3
2 3 7 -4
-1 -3 -6 -4
3 4 7 7
r2-2r1,r3+r1,r4-3r1
1 2 4 3
0 -1 -1 -10
0 -1 -2 -1
0 -2 -5 1
r3-r2,r4-2r2
1 2 4 3
0 -1 -1 -10
0 0 -1 9
0 0 -3 21
r4-3r3
1 2 4 3
0 -1 -1 -10
0 0 -1 9
0 0 0 -6
向量组的秩为4,极大无关组是其自身 a1,a2,a3,a4.

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