# rref, rrefmovie

## Purpose

Reduced row echelon form.

## Synopsis

    R = rref(A)
    R = rref(A,tol)
    R = rrefmovie(A)

## Description

`R` `=` `rref(A)` produces the reduced row echelon form of `A` using Gauss Jordan elimination with partial pivoting. A default tolerance of

    tol = max(size(A))*eps*norm(A,inf)

is used to test for negligible column elements.

`R` `=` `rref(A,tol)` uses `tol` for the tolerance.

`R` `=` `rrefmovie(A)` shows a movie of the algorithm working.

## Examples

Use `rref` on a rank-deficient magic square:

    A = magic(4), R = rref(A)

    A =
       16    2    3   13
        5   11   10    8
        9    7    6   12
        4   14   15    1

    R =
        1    0    0    1
        0    1    0    3
        0    0    1   -3
        0    0    0    0

## See Also

    inv, lu, rank

(c) Copyright 1994 by The MathWorks, Inc.