 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2009/paper-2/4/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

Zero is an eigenvalue exactly when the determinant vanishes. Here

det A = 1 - α^{2}

, so

α = 1 or α = - 1.

For either value the other eigenvalue is two, as follows from the trace.

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