Past exam of the mathematics course of the University of Oxford / 2023 / Prelims / Mathematics I / 1 / a / i

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- Solution i

Solution

The three elementary row operations on an

m \times n

real matrix are:

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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