设有向量组a1=(1,1,2,-1)T,a2=(-2,-1,-3,4)T,a3=(1,0,2,-3)T,a4=(0,1,2,2)T,a5=(1,2,1,1)T求向量组a1,a2,a3,a4,a5的秩.求向量组a1,a2,a3,a4,a5的一个极大线性无关组,并将其余向量用此极大线性无关组线性表示.我初等行
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![设有向量组a1=(1,1,2,-1)T,a2=(-2,-1,-3,4)T,a3=(1,0,2,-3)T,a4=(0,1,2,2)T,a5=(1,2,1,1)T求向量组a1,a2,a3,a4,a5的秩.求向量组a1,a2,a3,a4,a5的一个极大线性无关组,并将其余向量用此极大线性无关组线性表示.我初等行](/uploads/image/z/13368480-24-0.jpg?t=%E8%AE%BE%E6%9C%89%E5%90%91%E9%87%8F%E7%BB%84a1%3D%281%2C1%2C2%2C-1%29T%2Ca2%3D%28-2%2C-1%2C-3%2C4%29T%2Ca3%3D%281%2C0%2C2%2C-3%29T%2Ca4%3D%280%2C1%2C2%2C2%29T%2Ca5%3D%281%2C2%2C1%2C1%29T%E6%B1%82%E5%90%91%E9%87%8F%E7%BB%84a1%2Ca2%2Ca3%2Ca4%2Ca5%E7%9A%84%E7%A7%A9.%E6%B1%82%E5%90%91%E9%87%8F%E7%BB%84a1%2Ca2%2Ca3%2Ca4%2Ca5%E7%9A%84%E4%B8%80%E4%B8%AA%E6%9E%81%E5%A4%A7%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3%E7%BB%84%2C%E5%B9%B6%E5%B0%86%E5%85%B6%E4%BD%99%E5%90%91%E9%87%8F%E7%94%A8%E6%AD%A4%E6%9E%81%E5%A4%A7%E7%BA%BF%E6%80%A7%E6%97%A0%E5%85%B3%E7%BB%84%E7%BA%BF%E6%80%A7%E8%A1%A8%E7%A4%BA.%E6%88%91%E5%88%9D%E7%AD%89%E8%A1%8C)
设有向量组a1=(1,1,2,-1)T,a2=(-2,-1,-3,4)T,a3=(1,0,2,-3)T,a4=(0,1,2,2)T,a5=(1,2,1,1)T求向量组a1,a2,a3,a4,a5的秩.求向量组a1,a2,a3,a4,a5的一个极大线性无关组,并将其余向量用此极大线性无关组线性表示.我初等行
设有向量组a1=(1,1,2,-1)T,a2=(-2,-1,-3,4)T,a3=(1,0,2,-3)T,a4=(0,1,2,2)T,a5=(1,2,1,1)T
求向量组a1,a2,a3,a4,a5的秩.
求向量组a1,a2,a3,a4,a5的一个极大线性无关组,并将其余向量用此极大线性无关组线性表示.
我初等行变换换不出最下面一行都是0的情况 .
设有向量组a1=(1,1,2,-1)T,a2=(-2,-1,-3,4)T,a3=(1,0,2,-3)T,a4=(0,1,2,2)T,a5=(1,2,1,1)T求向量组a1,a2,a3,a4,a5的秩.求向量组a1,a2,a3,a4,a5的一个极大线性无关组,并将其余向量用此极大线性无关组线性表示.我初等行
(a1,a2,a3,a4,a5)=
1 -2 1 0 1
1 -1 0 1 2
2 -3 2 2 1
-1 4 -3 2 1
r2-r1,r3-2r1,r4+r1
1 -2 1 0 1
0 1 -1 1 1
0 1 0 2 -1
0 2 -2 2 2
r1+2r2,r3-r2,r4-2r2
1 0 -1 2 3
0 1 -1 1 1
0 0 1 1 -2
0 0 0 0 0
r1+r3,r2+r3
1 0 0 3 1
0 1 0 2 -1
0 0 1 1 -2
0 0 0 0 0
所以 r(a1,a2,a3,a4,a5)=3,a1,a2,a3 是一个极大无关组
a4 = 3a1+2a2+a3
a5 = a1-a2-2a3