GATE_AE_2027_MOCK_02_Q12 GATE 2027 Aerospace Engineering All-India Master Mock 02 (Compressible Aerodynamics & High-Speed Propulsion) NAT · 1 Mark
Engineering Mathematics • Linear Algebra • Eigenvalues and Eigenvectors

What is the sum of the eigenvalues of the matrix $M = \begin{pmatrix} 7 & -2 & 1 \\ -2 & 5 & 3 \\ 1 & 3 & 4 \end{pmatrix}$?

Answer Key:
16

Step-by-Step Verified Solution

### Solution: The sum of eigenvalues equals the trace of the matrix: $\text{Trace}(M) = 7 + 5 + 4 = 16$. Correct: 16.
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