Determine the eigenvalues of the matrix A = |-5 3 3| |-3 1 3| |-6 6 4|

Question

Determine the eigenvalues of the matrix

A = |-5 3 3|

|-3 1 3|

|-6 6 4|

Answer 1

det(A - λI) = 0; (- 5 - λ)(1 - λ)(4 - λ) - 54 - 54 + 18(1 - λ) + 18(5 + λ) + 9(4 - λ) = 0;

(- 5 - λ)(1 - λ)(4 - λ) + 9(4 - λ) = 0; (4 - λ)(λ² + 4λ + 4) = 0;

λ = 4 or λ = - 2 multiplicity 2