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RowReduce

RowReduce[m]
gives the row-reduced form of the matrix m.

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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 k rows and more than k columns, then the first k 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.

The possible settings for the Method option are as for LinearSolve.

Basic Examples (3)

Do row reduction on a square matrix:

Out[2]//MatrixForm=

Do row reduction on a rectangular matrix:

Out[2]//MatrixForm=

Applications (2)

Properties & Relations (3)

LinearSolve Inverse NullSpace GroebnerBasis

Solving Linear Systems

Implementation notes: Numerical and Related Functions

Linear Systems

Matrices and Linear Algebra

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