Question

n维列向量组a1...an线性无关 A是n阶方阵 如果Aa1...Aan线性相关 则|A|=?

Answer 1

因为 n维列向量组a1...an线性无关
所以 |a1,...,an| ≠ 0
同理 |Aa1,...,Aan| =0
而 A(a1,...,an) = (Aa1,...,Aan)
所以 |A| |a1,...,an| = |Aa1,...,Aan| = 0.
故有 |A| = 0.