 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-2-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-2/6/c/solution

The required contractions are

s = A^{T} A = 5, T A = 1090 - 70, q = A^{T} T A = 250, τ = 100.

α = 25, β = 5, B = 2 - 2 - 4, C = - 15 1632 163632612 .

Indeed

A^{T} B = - 4 + 4 = 0

C A = 0

and

tr C = - 15 + 3 + 12 = 0

. Adding

25 I + 5 A A^{T} + B A^{T} + A B^{T} + C

reconstructs the given tensor.

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