 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2011/paper-2/14/a/ii/solution

The characteristic polynomial, using the convention

det (λ I - A)

, is

p (λ) = λ^{3} + λ^{2} - 21 λ - 45 = (λ - 5) (λ + 3)^{2} .

5, - 3, - 3 .

Their product is

45

and their sum is

- 1

, agreeing with the determinant and trace of the matrix.

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