设A是三阶矩阵,a1,a2,a3,都是三维向量,满足|a1,a2,a3|不等于0.已知Aa1=a1+a2,Aa2=-a1+2a2-a3,Aa3=a2-3a3,求|A|.
问题描述：
设A是三阶矩阵,a1,a2,a3,都是三维向量,满足|a1,a2,a3|不等于0.已知Aa1=a1+a2,Aa2=-a1+2a2-a3,Aa3=a2-3a3,
求|A|.
答
A(a1,a2,a3)=(a1+a2,-a1+2a2-a3,a2-3a3)=(a1,a2,a3)K
K=
1 -1 0
1 2 1
0 -1 -3
等式两边取行列式,由于 |a1,a2,a3|≠0,所以
|A| = |K| = -8.