GATE 2024 Chemical Engineering, Q30 · Mathematics
The correct answer is -2.
Question
Consider a matrix A = [[−5, a], [−2, −2]], where a is a constant. If the eigenvalues of A are −1 and −6, then the value of a, rounded off to the nearest integer, is ____________
Official answer: -2
Why
GATE 2024 official key: −2. det(A) = (−5)(−2) − a(−2) = 10 + 2a must equal the product of eigenvalues (−1)(−6) = 6, so 10 + 2a a = −2.
Explanation cross-checked for consistency. Final answer matches the official IIT answer key.