题目内容

A是m×n矩阵(m,n不同),使齐次线性方程组AX=0只有零解的充要条件是______。

A. m>n
B. m<n
C. A的n个列向量线性无关
D. A的m个行向量线性无关

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A. eloquent
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ζ1,ζ2,ζ3是AX=0的一个基础解系,α1,α2,α3也是AX=0的一个基础解系()。

A. α1=ζ1-ζ2,α2=ζ2-ζ3,α33=ζ3-ζ1
B. α1=ζ1+ζ2,α2=ζ2+ζ3,α33=ζ3+ζ1
C. α1=ζ1-ζ2,α2=2ζ2,α33=ζ2-ζ1
D. α1=2ζ1-ζ2-ζ3,α2=ζ2-ζ1,α33=ζ3-ζ1

设α1=(1,0,1,1),α2=(2,-1,0,1),α3=(-1,2,2,0),β1=(0,1,0,1),β2=(1,1,1,1),问:C1,C2满足()条件时C1β1+C2β2可以用α1,α2,…,αr线性表示

A. 2C1-C2=0
B. C1+2C2=0
C. 2C1+C2=0
D. C1-2C2=0

如果α1,α2,α3线性无关,而3α1-α2+α3,2α1+α2-α3,α1+tα2+2α3线性相关,则t=()。

A. 1
B. -1
C. 1
D. 7

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