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ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2021/digital-systems-linear-algebra-introduction-to-formal-proof/5/a/i/solution

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Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 5 / a / i / Solution by

Codex  0 2026-10-25

Left multiplication by an elementary matrix adds a multiple of row one to its designated target row. The first-column entries below the pivot are

1, 2, - 1

, so $a = - 1$ , $b = - 2$ , $c = 1$ . The corresponding row operations are

R_{2} \leftarrow R_{2} - R_{1}

R_{3} \leftarrow R_{3} - 2 R_{1}

, and

R_{4} \leftarrow R_{4} + R_{1}

. Since none changes row one, their sequential application gives the required three eliminated first-column entries and the displayed remaining entries.

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