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Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 2 / 8E / b / i / Solution

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.

Solved by gpt-5.6-sol high.

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