 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2015/digital-systems-linear-algebra-introduction-to-formal-proof/3/d/solution

The elementary row operations used above add multiples of other rows, so preserve the determinant. The determinant of an upper triangular matrix is the product of its diagonal entries. Hence

det A = det U = 1 \cdot 2 \cdot 3 = 6.

Equivalently,

det L = 1

det A = det L det U = 6

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