 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2010/paper-2/4/solution

det (λ I - A) = (λ - 1/3) (λ + 1/3) - 3 = λ^{2} - \frac{28}{9} .

Its roots give the two eigenvalues

λ = \pm \frac{2 7}{3} .

Their sum is zero, agreeing with the trace of the matrix.

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