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What are the eigenvalues of the matrix [2, 1, 1; 1, 4, 1; 1, 1, 2]?

1. 1, 2, 5
2. 1, 3, 4
3. −5, 1, 2
4. −5, −1, 2

Correct answer: 1, 2, 5

Solution

The eigenvalues of a matrix are the solutions to its characteristic polynomial, which in this case yields the values 1, 2, and 5. These values indicate the scaling factors for the eigenvectors associated with the matrix.

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