GATE 2015 EC – Question 15
The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigenvector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is ________.
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Correct answer: 16.5 to 17.5
Explanation
Multiply the matrix by the vector. The first row gives $4 + 2 + 6 = 12$, so the eigenvalue is 12. The second row gives $p + 4 + 3 = p + 7$, which must equal $12 \times 2 = 24$, so $p = 17$.