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Let g(y) = det of the 3x3 matrix with rows [p-y, q, r], [r, p-y, q], [q, r, p-y], where p > q > r > 0. Find the coefficient of y (the linear term) in the expansion of g(y).
- independent of only p
- independent of q as well as r
- independent of only r
- none of these
Correct answer: none of these
Solution
After expanding the determinant, the coefficient of the linear term in y is 3(qr - p²), which depends on both p and q and r simultaneously, so none of the first three options is correct.
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