Let
be a matrix.
Then
,
, and
are respectively called the first, the second, and the third *row* of the
matrix .
And
,
, and
are respectively called the first, the second, and the third *column*
of the matrix .

Given a matrix , the following three basic row operations are used to systematically produce a reduced echelon form:

- Add a multiple of the -th row by to the -th row.
- Interchange the -th row and the -th row.
- Multiply the -th row by .

Given a matrix `C` in Matlab/Octave,
the above three row operations are carried out as follows:

`C(j,:) = C(j,:) + k * C(i,:)``C([j,i],:) = C([i,j],:)``C(i,:) = k * C(i,:)`

Department of Mathematics