GATE 2024 BT – Question 62
If $\vec v = \begin{pmatrix}2\\2\\2\end{pmatrix}$ is an eigenvector of the matrix $\begin{pmatrix}1&2&3\\1&2&3\\1&2&3\end{pmatrix}$ corresponding to the non-zero eigenvalue, $\lambda$, then the value of $\lambda$ is ________.
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Correct answer: 6
Explanation
Each row of the matrix times $\vec v$ gives $2 + 4 + 6 = 12$, so $A\vec v = (12, 12, 12) = 6\vec v$ and $\lambda = 6$.