GATE 2025 Chemical Engineering, Q45 · Mathematics
The correct answer is 3.68 to 3.78.
Question
Consider the matrix A = [[2, 3], [1, 2]]. The eigenvalues of the matrix are 0.27 and ____ (rounded off to 2 decimal places).
Official answer: 3.68 to 3.78
Why
GATE 2025 official key: 3.68 to 3.78. The trace equals the sum of eigenvalues: tr(A) = 2+2 = 4, so the second eigenvalue = 4 − 0.27 = 3.73.
Explanation cross-checked for consistency. Final answer matches the official IIT answer key.