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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2016/digital-systems-linear-algebra-introduction-to-formal-proof-resit/5/d/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2016 / Digital systems, linear algebra, introduction to formal proof (resit) / 5 / d / Solution by

Codex  0 2026-10-31

The determinant of the unit lower triangular matrix

L

is 1. There is one row swap, so

det P = - 1

, and the upper triangular matrix has determinant

1 \cdot (- 2) \cdot (3/2) \cdot 2 = - 6

. Therefore

det A = det P det L det U = 6.

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