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Given a - 2b + c = 1, let f(x) be the determinant with rows (x+a, x+2, x+1), (x+b, x+3, x+2), (x+c, x+4, x+3). Which is correct?

1. f(-50) = 501
2. f(-50) = -1
3. f(50) = 1
4. f(50) = -501

Correct answer: f(50) = 1

Solution

Row/column reduction shows f(x) = a - 2b + c for all x, so f is the constant 1; hence f(50) = 1.

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