 interactive Gauss-Jordan elimination - Maple Programming Help

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Student[LinearAlgebra][GaussJordanEliminationTutor] - interactive Gauss-Jordan elimination

 Calling Sequence GaussJordanEliminationTutor(M) GaussJordanEliminationTutor(M, v)

Parameters

 M - Matrix v - Vector

Description

 • The GaussJordanEliminationTutor(M) command allows you to interactively reduce the Matrix M to reduced row echelon form using Gauss-Jordan elimination.  You can then query for the rank, nullity, and bases for the row, column, and null spaces. It returns the reduced Matrix.
 • The GaussJordanEliminationTutor(M, v) command allows you to interactively solve the system $M·x=v$ by reducing the augmented Matrix  to reduced row echelon form using Gauss-Jordan elimination. It returns the solution as a column Vector.
 • Floating-point numbers in M or v are converted to rationals before computation begins.
 • The dimensions of the Matrix must be no greater than 5x5.

Examples

 > $\mathrm{with}\left({\mathrm{Student}}_{\mathrm{LinearAlgebra}}\right):$
 > $M≔⟨⟨1,2,0⟩|⟨2,3,2⟩|⟨0,2,1⟩|⟨3,5,5⟩⟩$
 ${M}{≔}\left[\begin{array}{cccc}{1}& {2}& {0}& {3}\\ {2}& {3}& {2}& {5}\\ {0}& {2}& {1}& {5}\end{array}\right]$ (1)
 > $v≔⟨5,4,2⟩$
 ${v}{≔}\left[\begin{array}{c}{5}\\ {4}\\ {2}\end{array}\right]$ (2)
 > $\mathrm{GaussJordanEliminationTutor}\left(M\right)$
 > $\mathrm{GaussJordanEliminationTutor}\left(M,v\right)$