 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/ib/paper-2/8e/b/i/solution

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

Choose the least

k \geq 1

such that

(f - α I)^{k} v = 0.

Then

w = (f - α I)^{k - 1} v

is nonzero by minimality, and

(f - α I) w = 0.

Therefore $f w = α w$ , so $w$ is the required nonzero eigenvector.

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