 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/c/solution

For

i \neq = j

R_{i} \leftarrow R_{i} - k R_{j}

det (\dots, R_{i} - k R_{j}, \dots, R_{j}, \dots) = det A .

i

, the left side is

det A

minus

k

j

appearing twice. That second determinant is zero by alternation. No row scaling or row interchange is involved.

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