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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 6C / a / Solution

The distinguished unit vector is

n = (1, 1, 1) / 3

. Comparing diagonal, symmetric off-diagonal, and antisymmetric parts gives

α = a - \frac{b + c}{2}, β = \frac{3}{2} (b + c), γ = \frac{3}{2} (b - c),

so

A_{ij} = α δ_{ij} + β n_{i} n_{j} + γ ε_{ijk} n_{k}

.

Solved by gpt-5.6-sol high.

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