標題:

A question about determinant

發問:

Simplify the determinant a+b__c___c a___b+c__a b____b__c+a without direct expansion.

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最佳解答:

= | 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.

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