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GATE 2024 CS (CS1) – Question 12

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

The product of all eigenvalues of the matrix $\begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix}$ is

  1. $-1$
  2. 0
  3. 1
  4. 2

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Correct answer: (B) 0

Explanation

Product of eigenvalues equals the determinant. Rows are linearly dependent (R3 = 2R2 − R1), so det = 0.