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Student[LinearAlgebra]

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

 Calling Sequence GaussianElimination(A) ReducedRowEchelonForm(A)

Parameters

 A - Matrix

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 command is equivalent to calling 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 command is equivalent to calling LUDecomposition with the output=['R'] option.

Examples

 > $\mathrm{with}\left(\mathrm{Student}[\mathrm{LinearAlgebra}]\right):$
 > $A≔⟨⟨8,3,-1,-5⟩|⟨4,-5,0,-2⟩|⟨-5,8,3,-1⟩|⟨-5,5,-4,-9⟩⟩$
 ${A}{≔}\left[\begin{array}{rrrr}{8}& {4}& {-}{5}& {-}{5}\\ {3}& {-}{5}& {8}& {5}\\ {-}{1}& {0}& {3}& {-}{4}\\ {-}{5}& {-}{2}& {-}{1}& {-}{9}\end{array}\right]$ (1)
 > $b≔⟨4,0,-8,-5⟩$
 ${b}{≔}\left[\begin{array}{r}{4}\\ {0}\\ {-}{8}\\ {-}{5}\end{array}\right]$ (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)
 > $\mathrm{ReducedRowEchelonForm}\left(⟨A|b⟩\right)$
 $\left[\begin{array}{ccccc}{1}& {0}& {0}& {0}& \frac{{1715}}{{2607}}\\ {0}& {1}& {0}& {0}& {-}\frac{{3668}}{{2607}}\\ {0}& {0}& {1}& {0}& {-}\frac{{1345}}{{869}}\\ {0}& {0}& {0}& {1}& \frac{{1759}}{{2607}}\end{array}\right]$ (4)