 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2007/paper-1/section-b/8/c/i/solution

Computing the characteristic polynomial with the convention

det (λ I - H)

gives

det (λ I - H) = λ (λ + 1) (λ - 3) .

Thus the three eigenvalues are

- 1, 0, 3.

They can also be checked directly on the respective eigenvectors

(1, 0, - 1)^{T}

(1, - 1, 1)^{T}

, and

(1, 2, 1)^{T}

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