向量组为(1,2,1,3),(4,-1,-5,6),(-1,-3,-4,-7),(2,1,2,9),求向...

(a1,a2,a3,a4) =
1 4 -1 2
2 -1 -3 1
1 -5 -4 2
3 6 -7 9
r2-2r1,r3-r1,r4-3r1
1 4 -1 2
0 -9 -1 -3
0 -9 -3 0
0 -6 -4 3
r3*(-1/3),r2+3r3,r4+2r3
1 4 -1 2
0 0 2 -3
0 3 1 0
0 0 -2 3
r4+r3
1 4 -1 2
0 0 2 -3
0 3 1 0
0 0 0 0
交换行
1 4 -1 2
0 3 1 0
0 0 2 -3
0 0 0 0
向量组的秩为3,a1,a2,a3 是一个极大无关组.