 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ia/paper-1/8b/c/solution

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

A = (x_{3} x_{1} + i x_{2} x_{1} - i x_{2} - x_{3})

, so

tr A = 0

and

det A = - ∣ x ∣^{2}

. Unitary conjugation preserves Hermiticity, trace, and determinant; every traceless Hermitian

2 \times 2

x' \cdot σ

with real

x'

, and

∣ x'∣ = ∣ x ∣

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