What are the eigenvalues of the matrix \(\begin{bmatrix} 2 & 1 & 1 \\[0.3em] 1 & 4 & 1 \\[0.3em] 1 & 2 & 2 \end{bmatrix}\)?
- 1, 2, 5
- 1, 3, 4
- -5, 1, 2
- -5, -1, 2
The Correct Option is A
Solution and Explanation
Top Questions on Eigenvalues
- The eigenvalues of the matrix \[ A = \begin{bmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{bmatrix} \] are \(\lambda_1, \lambda_2, \lambda_3\). The value of \(\lambda_1 \lambda_2 \lambda_3 (\lambda_1 + \lambda_2 + \lambda_3)\) is:
- The eigenvalues of the matrix \( A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \) are:
The eigenvalues of the matrix
are \( \lambda_1, \lambda_2, \lambda_3 \). The value of \( \lambda_1 \lambda_2 \lambda_3 ( \lambda_1 + \lambda_2 + \lambda_3 ) \) is:
- The eigenvalues of the matrix: \[ \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \] are ________
Let \[ A = \begin{pmatrix} 1 & 0 & 1 \\ 0 & k & 0 \\ 3 & 0 & -1 \end{pmatrix}. \] If the eigenvalues of \( A \) are -2, 1, and 2, then the value of \( k \) is _.
(Answer in integer)
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