作业帮已知A是3阶矩阵,a1,a2,a3是3维线性无关列向量,Aa1=a1+2a3,
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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
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
A(a1,a2,a3) = (Aa1,Aa2,Aa3) = (a1,a2,a3)K
K=
1 0 2
0 1 2
2 2 -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|
= -9 |a1+2a3, a2+2a3, a3|
= -9 |a1,a2,a3|
所以 |A| = -9.
K=
1 0 2
0 1 2
2 2 -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|
= -9 |a1+2a3, a2+2a3, a3|
= -9 |a1,a2,a3|
所以 |A| = -9.
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