## Row operations

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:

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

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

1. C(j,:) = C(j,:) + k * C(i,:)
2. C([j,i],:) = C([i,j],:)
3. C(i,:) = k * C(i,:)

Department of Mathematics