 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/digital-systems-linear-algebra-introduction-to-formal-proof/6/d/solution

A triangular matrix has determinant equal to the product of its diagonal entries. Since

L

det L = 1

. Thus

det A = det L det U = 1 \cdot (1 \cdot 4 \cdot (- 1)) = - 4.

Equivalently, the elimination used only row additions, which leave the determinant unchanged; there were no row swaps or row scalings to account for.

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