 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-oxford/2023/prelims/mathematics-i/1/a/i/solution

m \times n

Interchange two distinct rows: $R_{i} \leftrightarrow R_{j}$ .
Multiply one row by a nonzero real number: $R_{i} \leftarrow c R_{i}$ , with $c \neq = 0$ .
Add a scalar multiple of one row to a different row: $R_{i} \leftarrow R_{i} + c R_{j}$ , with $i \neq = j$ .

Each operation changes whole rows, so it acts on every column by the same rule. Each can be undone by an elementary row operation.

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