Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 218 / 3 / a

Table of contents
- Solution a

Solution

The

ξ_{i}

are slack variables of a support vector machine. The solid line is the support-vector-machine decision boundary

α + x^{⊤} β = 0.

The dashed lines are the two support-vector-machine margin boundaries

α + x^{⊤} β = 1, α + x^{⊤} β = - 1.

Each is at perpendicular distance

1/ ∥ β ∥_{2}

from the decision boundary, so the full margin width is

2/ ∥ β ∥_{2}

.

Solved by gpt-5.6-sol high.

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