# RowReduce

RowReduce[m]

gives the rowreduced form of the matrix m.

# Details 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.

# Examples

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## Basic Examples(3)

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Do row reduction on a square matrix:

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Do row reduction on a rectangular matrix:

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