 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2003/calculus-probability-linear-algebra-discrete-mathematics-logic-and-proof-and-models-of-computation/4/a/i/solution

interchange two distinct rows, $R_{i} \leftrightarrow R_{j}$ ;
multiply a row by a nonzero scalar, $R_{i} \leftarrow c R_{i}$ with $c \neq = 0$ ;
add a scalar multiple of another row, $R_{i} \leftarrow R_{i} + c R_{j}$ with $i \neq = j$ .

The nonzero requirement in the second operation ensures that each elementary row operation is reversible.

R_{i} \leftrightarrow R_{j}; R_{i} \leftarrow c R_{i} (c \neq = 0); R_{i} \leftarrow R_{i} + c R_{j} (i \neq = j) .

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