 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ii/paper-3/17j/a/i/solution

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

A v = λ v

, choose

i

with

∣ v_{i} ∣

maximal. Then

∣ λ ∣∣ v_{i} ∣ = ∣ \sum_{j \sim i} v_{j} ∣ \leq d (i) ∣ v_{i} ∣ \leq Δ∣ v_{i} ∣

, so

∣ λ ∣ \leq Δ

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