 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2013/digital-systems-linear-algebra-introduction-to-formal-proof/4/b/solution

det T = i = 1 \prod n T_{ii} .

In the permutation formula for the determinant, every contribution except the diagonal product includes an entry on the zero side of the diagonal. Equivalently, successive cofactor expansions along the first column of an upper triangular matrix prove the formula by mathematical induction.

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