MATLAB Function Reference |

**Syntax**

**Description**

produces the reduced row echelon form of ```
R = rref(A)
```

`A`

using Gauss Jordan elimination with partial pivoting. A default tolerance of (`max(size(A))*eps *norm(A,inf)`

) tests for negligible column elements.

also returns a vector ```
[R,jb] = rref(A)
```

`jb`

such that:

`r = length(jb)`

is this algorithm's idea of the rank of`A`

.`x(jb)`

are the pivot variables in a linear system`Ax = b`

.`A(:,jb)`

is a basis for the range of`A`

.`R(1:r,jb)`

is the`r`

-by-`r`

identity matrix.

```
[R,jb] = rref(A,tol)
```

uses the given tolerance in the rank tests.

Roundoff errors may cause this algorithm to compute a different value for the rank than `rank`

, `orth`

and `null`

.

**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**

round | rsf2csf |