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:
  • MethodAutomaticmethod to use
    Modulus0integer modulus to use
    ToleranceAutomaticnumerical tolerance to use
    ZeroTestAutomaticfunction 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:

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Do row reduction on a rectangular matrix:

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