 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2005/paper-1/2/a/solution

Codex  0 Created 2026-10-18 Updated 2026-10-20

True. The symmetric and antisymmetric parts of a matrix are, in Einstein summation convention,

S_{ij} = \frac{M _{ij} + M _{ji}}{2}, A_{ij} = \frac{M _{ij} - M _{ji}}{2} .

They satisfy

S_{ji} = S_{ij}

A_{ji} = - A_{ij}

and

S_{ij} + A_{ij} = M_{ij}

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