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Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 1 / 6C / e / Solution

The line/plane decomposition gives

det A = (α + β) (α^{2} + γ^{2}) .

Substituting the values in part (a) and simplifying yields

det A = \frac{1}{2} (a + b + c) ((a - b)^{2} + (b - c)^{2} + (c - a)^{2}) .

Solved by gpt-5.6-sol high.

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