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If a, b, c are the sides of a scalene triangle, what is the value of the determinant | a b c; b c a; c a b |?
- non-negative
- negative
- positive
- non-positive
Correct answer: negative
Solution
The circulant determinant equals 3abc - a³ - b³ - c³ = -(a+b+c)*(1/2)*[(a-b)²+(b-c)²+(c-a)²]; for a scalene triangle a+b+c > 0 and the bracket > 0, so it is negative.
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