By using pivot positions and basic row operations, the following procedure produces a reduced echelon form (REF).
The size of pivot positions used in the above procedure is called the rank of , denoted by rank.
EXAMPLE 1. Apply row operations to reduce the following matrix to an echelon form.
EXAMPLE 2. Apply row operations to transform the following matrix first into an echelon form, and then reduce it into the reduced echelon form.
Matlab comes with a rref function for row reducing matrices. For Octave you can download rref.m from our web site, and place it into your working directory. Provided an augmented matrix A, type
> rref(A)which produces a REF.
In Matlab/Octave the function rank(A) can be called to compute the rank of matrix A.