GATE 2024 ES – Question 24
Select the eigenvalues of $\begin{pmatrix}4&3\\3&4\end{pmatrix}$.
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Correct answer: (A) 1; (C) 7
Explanation
The characteristic equation is $(4-\lambda)^2-9=0$,so $4-\lambda=\pm3$ and eigenvalues are1,7. Equivalently, vectors(1,1) and(1,−1) have eigenvalues7 and 1. Select **A, C**; the sum8 and product7 match trace and determinant.