# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# RowReduce

RowReduce[m]
gives the rowreduced form of the matrix m.

## Details and OptionsDetails and Options

• RowReduce performs a version of Gaussian elimination, adding multiples of rows together so as to produce zero elements when possible. The final matrix is in reduced row echelon form.
• If m is a nondegenerate square matrix, RowReduce[m] is IdentityMatrix[Length[m]]. »
• If m is a sufficiently nondegenerate rectangular matrix with rows and more than columns, then the first columns of RowReduce[m] will form an identity matrix. »
• RowReduce works on both numerical and symbolic matrices.
• The following options can be given:
•  Method Automatic method to use Modulus 0 integer modulus to use Tolerance Automatic numerical tolerance to use ZeroTest Automatic function to test whether matrix elements should be considered to be zero
• RowReduce[m,Modulus->n] performs row reduction modulo n. »
• RowReduce[m,ZeroTest->test] evaluates test[m[[i,j]]] to determine whether matrix elements are zero.
• Possible settings for the Method option include "CofactorExpansion", "DivisionFreeRowReduction", and "OneStepRowReduction". The default setting of Automatic switches among these methods depending on the matrix given.

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

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Do row reduction on a square matrix:

 In[1]:=
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 In[2]:=
 Out[2]//MatrixForm=

Do row reduction on a rectangular matrix:

 In[1]:=
 Out[1]=
 In[2]:=
 Out[2]//MatrixForm=

## TutorialsTutorials

Introduced in 1988
(1.0)
| Updated in 1996
(3.0)