GATE 2014 CS (CS2) – Question 57
Find the product of nonzero eigenvalues of $\begin{pmatrix}1&0&0&0&1\\0&1&1&1&0\\0&1&1&1&0\\0&1&1&1&0\\1&0&0&0&1\end{pmatrix}$.
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Correct answer: 6 to 6
Explanation
Reordering coordinates separates a2by2all-ones block from a3by3all-ones block. Their eigenvalues are2,0 and3,0,0respectively. The nonzero eigenvalues multiply to **2×3=6**. The full determinant is zero and is not the requested product.