Simplify the determinant
a+b__c___c
a___b+c__a
b____b__c+a
without direct expansion.
A question about determinant
2012-08-28 4:18 am
回答 (1)
2012-08-28 4:08 pm
✔ 最佳答案
= | 0 - 2b - 2a | (R1 - R2 - R3) to R1| a b + c a |
| b b c + a |
= 2 | 0 - b - a |
| a b + c a |
| b b c + a |
= 2 | 0 0 - a | (C2 - C3 x b/a) to C2
| a (b + c) - b a |
| b b - b(c + a)/a c + a |
= - 2 a | a c |
| b - bc/a |
= - 2 a ( - bc - bc) = (-2a)(-2bc) = 4abc.
收錄日期: 2021-04-25 22:39:39
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120827000051KK00826