 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ii/paper-4/30j/b/solution

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

S \subseteq R^{d}

conv S = {\sum_{j = 1}^{m} λ_{j} v_{j} : m < \infty, v_{j} \in S, λ_{j} \geq 0, \sum_{j = 1}^{m} λ_{j} = 1} .

Thus

v

v_{1}, \dots, v_{m}

when it has precisely this form. Equivalently,

conv S

is the smallest convex set containing

S

R^{d}

: every point of

conv S

d + 1

points of

S

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