Question

a1=(2, -5, 1, 2) a2=(-3, -10, 4, -4)

a1=(1,-2,5,3),a2=(4,-1,-2,3),a3=(5,4,-19,15),a4=(-10,-1,16,-15)求向量组的秩,
向量组的一个极大无关组,用选定地极大无关组表示其他向量

Answer 1

(a1^T,a2^T,a3^T,a4^T)
1 4 5 -10
-2 -1 4 -1
5 -2 -19 16
3 3 15 -15
r2+2r1,r3-5r1,r4-3r1
1 4 5 -10
0 7 14 -21
0 -22 -44 66
0 -9 0 15
r2*(1/7),r3*(1/22)
1 4 5 -10
0 1 2 -3
0 -1 -2 3
0 -9 0 15
r1-4r2,r3+r2,r4+9r2
1 0 -3 2
0 1 2 -3
0 0 0 0
0 0 18 -12
r4*(1/18),r1+3r4,r2-2r4
1 0 0 0
0 1 0 -5/3
0 0 0 0
0 0 1 -2/3
向量组的秩为3, a1,a2,a3是一个极大无关组
a4 = (-5/3)a2 - (2/3)a3.