 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-1/7a/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

With

χ_{A} (t) = det (t I - A)

, direct expansion gives

χ_{A} (t) = (t - 3) (t - 1)^{2} (t + 1) (t + 2) .

Thus the eigenvalues are $3, 1, - 1, - 2$ . Kernel calculation gives eigenspace dimensions $1, 2, 1, 1$ , respectively.

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