已知A是3阶矩阵,a1,a2,a3是3维线性无关列向量,Aa1=a1+2a3,

问题描述:

已知A是3阶矩阵,a1,a2,a3是3维线性无关列向量,Aa1=a1+2a3,
接标题
Aa2=a2+2a3,Aa3=2a1+2a2-a3,则行列式|A|=?

A(a1,a2,a3)= (a1,a2,a3)K
K =
1 0 2
0 1 2
2 2 -1
所以 |A||a1,a2,a3|= |a1,a2,a3||K|.
由a1,a2,a3线性无关,所以 |a1,a2,a3| ≠ 0.
所以 |A| = |K| = -1 -4 -4 = -9.