Definition RO Row Operations

The following three operations will transform an $m\times n$ matrix into a different matrix of the same size, and each is known as a row operation.

1. Swap the locations of two rows.
2. Multiply each entry of a single row by a nonzero quantity.
3. Multiply each entry of one row by some quantity, and add these values to the entries in the same columns of a second row. Leave the first row the same after this operation, but replace the second row by the new values.

We will use a symbolic shorthand to describe these row operations:

1. $\rowopswap{i}{j}$: Swap the location of rows $i$ and $j$.
2. $\rowopmult{\alpha}{i}$: Multiply row $i$ by the nonzero scalar $\alpha$.
3. $\rowopadd{\alpha}{i}{j}$: Multiply row $i$ by the scalar $\alpha$ and add to row $j$.