 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2016/ib/paper-1/9f/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-06

A, B

r, s \in F

, the definition of the trace gives

Tr (r A + s B) = \sum_{i} (r a_{ii} + s b_{ii}) = r Tr (A) + s Tr (B) .

Hence the trace is a linear functional on the vector space of

n \times n

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