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An Eigen value of the matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ is $1$. An eigen vector corresponding to it is:}

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To quickly verify an option vector as an eigenvector in competitive examinations, multiply the matrix $A$ directly by the choice vectors. Whichever choice yields a scalar multiple of itself ($AX = 1 \cdot X$) is the correct response.

Updated On: Jun 25, 2026

$\begin{bmatrix} 3 \\ 2 \\ 0 \end{bmatrix}$
$\begin{bmatrix} 4 \\ 2 \\ -1 \end{bmatrix}$
$\begin{bmatrix} -4 \\ 2
1 \end{bmatrix}$
$\begin{bmatrix} 3 \\ 0
1 \end{bmatrix}$

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The Correct Option is C

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An Eigen value of the matrix $\begin{bmatrix} 1 & -1 & 2 \\ 0 & 1 & 0 \\ 1 & 2 & 1 \end{bmatrix}$ is $1$. An eigen vector corresponding to it is:}

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The Correct Option is C

Solution and Explanation

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