求向量组a1=(1,2,1,3),a2=(4,-1,-5,-6),a3=(-1,-3,-4,-7),a4=(2,1,2,
求向量组a1=(1,2,1,3),a2=(4,-1,-5,-6),a3=(-1,-3,-4,-7),a4=(2,1,2,3)的一个极大线性无关组,并把其余
向量用极大无关组线性表出
向量用极大无关组线性表出
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(a1^T,a2^T,a3^T,a4^T)=
1 4 -1 2
2 -1 -3 1
1 -5 -4 2
3 -6 -7 3
r4-r2-r3,r2-2r1,r3-r1
1 4 -1 2
0 -9 -1 -3
0 -9 -3 0
0 0 0 0
r3-r2
1 4 -1 2
0 -9 -1 -3
0 0 -2 3
0 0 0 0
r3*(-1/2),r1+r3,r2+r3
1 4 0 1/2
0 -9 0 -9/2
0 0 1 -3/2
0 0 0 0
r2*(-1/9),r1-4r2
1 0 0 -3/2
0 1 0 1/2
0 0 1 -3/2
0 0 0 0
a1,a2,a3是一个极大无关组.
且 a4 = (-3/2)a2+(1/2)a2-(3/2)a3.
1 4 -1 2
2 -1 -3 1
1 -5 -4 2
3 -6 -7 3
r4-r2-r3,r2-2r1,r3-r1
1 4 -1 2
0 -9 -1 -3
0 -9 -3 0
0 0 0 0
r3-r2
1 4 -1 2
0 -9 -1 -3
0 0 -2 3
0 0 0 0
r3*(-1/2),r1+r3,r2+r3
1 4 0 1/2
0 -9 0 -9/2
0 0 1 -3/2
0 0 0 0
r2*(-1/9),r1-4r2
1 0 0 -3/2
0 1 0 1/2
0 0 1 -3/2
0 0 0 0
a1,a2,a3是一个极大无关组.
且 a4 = (-3/2)a2+(1/2)a2-(3/2)a3.
1年前
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