设A为三阶矩阵,Aj是A的第j列(j=1,2,3)矩阵B=(A3,3A2-A3,2A1+5A2),若|A|=-2.B等于多少
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解决时间 2021-04-13 15:40
- 提问者网友：抽煙菂渘情少年
- 2021-04-12 17:45
设A为三阶矩阵,Aj是A的第j列(j=1,2,3)矩阵B=(A3,3A2-A3,2A1+5A2),若|A|=-2.B等于多少
最佳答案
- 五星知识达人网友：西岸风
- 2021-04-12 19:02
| A3,3A2-A3,2A1+5A2 |
c2+c1
= | A3,3A2,2A1+5A2 |
= 3 | A3,A2,2A1+5A2 |
c3-5c2
= 3 | A3,A2,2A1 |
= 6 | A3,A2,A1 |
c1<->c3
= -6 | A1,A2,A3 |
= -6 |A|
= -6*(-2)
= 12.
高级解法就是转化为矩阵乘积的形式求行列式
B = (A3,3A2-A3,2A1+5A2) = (A1,A2,A3)K = AK
其中 K=
0 0 2
0 3 5
1 -1 0
|B| = |A||K| = -2 * (-6) = 12.
c2+c1
= | A3,3A2,2A1+5A2 |
= 3 | A3,A2,2A1+5A2 |
c3-5c2
= 3 | A3,A2,2A1 |
= 6 | A3,A2,A1 |
c1<->c3
= -6 | A1,A2,A3 |
= -6 |A|
= -6*(-2)
= 12.
高级解法就是转化为矩阵乘积的形式求行列式
B = (A3,3A2-A3,2A1+5A2) = (A1,A2,A3)K = AK
其中 K=
0 0 2
0 3 5
1 -1 0
|B| = |A||K| = -2 * (-6) = 12.
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