 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2025/paper-2/9/a/solution

An eigenvalue makes the shifted matrix singular, so its characteristic polynomial vanishes:

det (1 - λ 1 1 2 - λ) = (1 - λ) (2 - λ) - 1.

λ^{2} - 3 λ + 1 = 0 .

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