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Elementary row operation

One of the following operations on the rows of a matrix:

interchange (swap)

exchange two rows
\(R_i \leftrightarrow R_j\)

scaling

replace a row a by a non-zero constant multiple of itself
\(R_i \gets kR_i\) with \(k \neq 0\)

replacement

replace any row a by the sum of itself and a multiple of another row
\(R_i \gets R_i + kR_j\) with \(i \neq j\)

• No change in solutions
• Reversibility