 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ia/paper-2/7c/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

det (A - λ I) = λ (λ - 1) .

For

λ_{1} = 0

and

λ_{2} = 1

, corresponding eigenvectors are

u_{1} = (21), u_{2} = (31) .

They are linearly independent, so the general homogeneous solution is

z (t) = α (21) + β e^{t} (31) .

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