 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ia/paper-1/6c/a/solution

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

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),

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

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