向量组a1,a2,…am，向量组线性无关的充要条件是R(A)=m怎么理解 谢谢

Question

如题所述

Answer 1

向量组的秩等于其一个极大无关组所含向量的个数
R(A)=m
<=> 极大无关组即向量组本身
<=> 向量组线性无关来自：求助得到的回答

Answer 2

if R(A) = n; n < m
=> there exists aj such that
aj = k1a1+k2a2+...+k(j-1)a(j-1)+k(j+1)a(j+1)+..+ kmam
then a1,a2,..,am is linearly dependent.