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LinearAlgebra

 GaussianElimination
 perform Gaussian elimination on a Matrix
 ReducedRowEchelonForm
 perform Gauss-Jordan elimination on a Matrix

 Calling Sequence GaussianElimination(A, m, options) ReducedRowEchelonForm(A, options)

Parameters

 A - Matrix m - (optional) equation of the form method = name where name is one of 'GaussianElimination', or 'FractionFree'; method used to factorize A options - (optional); constructor options for the result object

Description

 • The GaussianElimination(A) command performs Gaussian elimination on the Matrix A and returns the upper triangular factor U with the same dimensions as A.
 This function is equivalent to calling LinearAlgebra[LUDecomposition] with the output=['U'] option.
 • The ReducedRowEchelonForm(A) command performs Gauss-Jordan elimination on the Matrix A and returns the unique reduced row echelon form R of A.
 This function is equivalent to calling LinearAlgebra[LUDecomposition] with the output=['R'] option.
 • The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).
 • These functions are part of the LinearAlgebra package, and so it can be used in the form GaussianElimination(..) or ReducedRowEchelonForm(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[GaussianElimination](..) or LinearAlgebra[ReducedRowEchelonForm](..).

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
 > $A≔⟨⟨8,3,-1,-5⟩|⟨4,-5,0,-2⟩|⟨-5,8,3,-1⟩|⟨-5,5,-4,-9⟩⟩$
 ${A}{≔}\left[\begin{array}{cccc}{8}& {4}& {-5}& {-5}\\ {3}& {-5}& {8}& {5}\\ {-1}& {0}& {3}& {-4}\\ {-5}& {-2}& {-1}& {-9}\end{array}\right]$ (1)
 > $b≔⟨4,0,-8,-5⟩$
 ${b}{≔}\left[\begin{array}{c}{4}\\ {0}\\ {-8}\\ {-5}\end{array}\right]$ (2)
 > $\mathrm{GaussianElimination}\left(A\right)$
 $\left[\begin{array}{cccc}{8}& {4}& {-5}& {-5}\\ {0}& {-}\frac{{13}}{{2}}& \frac{{79}}{{8}}& \frac{{55}}{{8}}\\ {0}& {0}& \frac{{163}}{{52}}& {-}\frac{{213}}{{52}}\\ {0}& {0}& {0}& {-}\frac{{2607}}{{163}}\end{array}\right]$ (3)
 > $\mathrm{GaussianElimination}\left(A,'\mathrm{method}'='\mathrm{FractionFree}'\right)$
 $\left[\begin{array}{cccc}{8}& {4}& {-5}& {-5}\\ {0}& {-52}& {79}& {55}\\ {0}& {0}& {-163}& {213}\\ {0}& {0}& {0}& {2607}\end{array}\right]$ (4)
 > $\mathrm{ReducedRowEchelonForm}\left(⟨A|b⟩\right)$
 $\left[\begin{array}{ccccc}{1}& {0}& {0}& {0}& \frac{{1715}}{{2607}}\\ {0}& {1}& {0}& {0}& {-}\frac{{3668}}{{2607}}\\ {0}& {0}& {1}& {0}& {-}\frac{{1345}}{{869}}\\ {0}& {0}& {0}& {1}& \frac{{1759}}{{2607}}\end{array}\right]$ (5)