BUILT-IN MATHEMATICA SYMBOL

# RowReduce

RowReduce[m]
gives the row-reduced 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 non-degenerate square matrix, RowReduce[m] is IdentityMatrix[Length[m]]. »
• If m is a sufficiently non-degenerate 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 to determine whether matrix elements are zero.
• Possible settings for the Method option include , , and . 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:

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 Out[2]//MatrixForm=

Do row reduction on a rectangular matrix:

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 Out[2]//MatrixForm=