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-_数学解答

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|=?我会用相似法但是题目要求的用行列式性质和特征值这两种方法我不会啊老师

人气：130 ℃　时间：2020-02-05 22:33:47

解答

A(a1,a2,a3) = (Aa1,Aa2,Aa3) = (a1,a2,a3)KK=10201222 -1所以 |A| = |K| = -9.|A||a1,a2,a3| = |A(a1,a2,a3)| = |Aa1,Aa2,Aa3|= |a1+2a3, a2+2a3, 2a1+2a2-a3|c3 - 2c1 - 2c2= |a1+2a3, a2+2a3, -9a3|= -...