Matrix/Elementary row operation/Definition

Elementary row operations

Let ${}K$ be a field, and let ${}M$ be an ${}m\times n$-matrix over ${}K$. Then the following manipulations on ${}M$ are called elementary row operations.

1. Transpositions of two rows.
2. Multiplication of a row with a scalar ${}s\neq 0$.
3. Addition of ${}a$ times a row to another row.