求极大无关组,a1=1201,a2=3142,a3=-2031,a4=-33-11要求：初等行变换的具体步骤,到简化阶梯形为止

Question

求极大无关组,a1=1 2 0 1,a2=3 1 4 2,a3=-2 0 3 1,a4=-3 3 -1 1
要求：初等行变换的具体步骤,到简化阶梯形为止

Answer 1

A=(a1,a2,a3,4)
1 3 -2 -3
2 1 0 3
0 4 3 -1
1 2 1 1
r1-r4,r2-2r4
0 1 -3 -4
0 -3 -2 1
0 4 3 -1
1 2 1 1
r2+3r1,r3-4r1,r4-2r1
0 1 -3 -4
0 0 -11 -11
0 0 15 15
1 0 7 9
r2*(-1/11),r1+3r2,r3-15r2,r4-7r2
0 1 0 -1
0 0 1 1
0 0 0 0
1 0 0 2
交换行得
1 0 0 2
0 1 0 -1
0 0 1 1
0 0 0 0
a1,a2,a3 是一个极大无关组
a4 = 2a1-a2+a3