 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/11/c/solution

Choose two perpendicular unit directions in the

- 2

e_{1} = \frac{( 1 , 0 , 1 )}{2}, e_{2} = \frac{( 1 , 0 , - 1 )}{2}, e_{3} = (0, 1, 0) .

Their pairwise dot products vanish and their Euclidean norms are one. They form an orthonormal basis of eigenvectors, with eigenvalues

4, - 2, - 2

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