 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ia/paper-1/6c/c/solution

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

For

a = (a_{1}, a_{2}, a_{3})^{T}

A = 0 a_{3} - a_{2} - a_{3} 0 a_{1} a_{2} - a_{1} 0 .

Its diagonal is zero, so

tr A = 0

. Also

A a = a \times a = 0

, and

a \neq = 0

, so

A

has a nontrivial kernel. Hence

tr A = 0, det A = 0 .

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