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:
  • 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 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.
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