GaussJordanEliminationTutor - Maple Help

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Student[LinearAlgebra][GaussJordanEliminationTutor] - interactive and step-by-step Gauss-Jordan elimination

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

Parameters

 M - Matrix v - Vector opts - (optional) equation(s) of the form option=value where equation is output or displaystyle

Description

 • The GaussJordanEliminationTutor command by default opens a Maplet window which allows you to work interactively through Gauss-Jordan elimination. Options provide other ways to show the step-by-step solutions, as described below.
 • 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.
 • When the tutor is closed, the solution steps displayed in the tutor are re-displayed in the worksheet, with annotations showing the operations applied. Note that this display only and is not a value which can be further manipulated from within the worksheet. The value returned from the tutor, which can be used (for example, by referencing its equation label), is the state of the problem at the time the tutor was closed.
 • The following options can be used to control how the problem is displayed and what output is returned, giving the ability to generate step-by-step solutions directly without going through the Maplet tutor interface:
 – output = steps,canvas,script,record,list,print,printf,typeset,link (default: maplet)

The output options are described in Student:-Basics:-OutputStepsRecord.  Use output = steps to get the default settings for displaying ste

 – displaystyle= columns,compact,linear,brief (default: linear)

The displaystyle options are described in Student:-Basics:-OutputStepsRecord.

Examples

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right):$
 > $M≔⟨⟨1,2,0⟩|⟨2,3,2⟩|⟨0,2,1⟩|⟨3,5,5⟩⟩$
 ${M}{≔}\left[\begin{array}{cccc}{1}& {2}& {0}& {3}\\ {2}& {3}& {2}& {5}\\ {0}& {2}& {1}& {5}\end{array}\right]$ (1)
 > $v≔⟨5,4,2⟩$
 ${v}{≔}\left[\begin{array}{c}{5}\\ {4}\\ {2}\end{array}\right]$ (2)
 > $\mathrm{GaussJordanEliminationTutor}\left(M\right)$
 > $\mathrm{GaussJordanEliminationTutor}\left(M,v\right)$
 > $\mathrm{GaussJordanEliminationTutor}\left(M,\mathrm{output}=\mathrm{steps}\right)$
 $\begin{array}{lll}{}& {}& \text{Gauss-Jordan Reduce}\\ {}& {}& \left[\begin{array}{cccc}{1}& {2}& {0}& {3}\\ {2}& {3}& {2}& {5}\\ {0}& {2}& {1}& {5}\end{array}\right]\\ \text{•}& {}& \text{Subtract 2 times row 1 from row 2; (R2 = R2-2*R1)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {2}& {0}& {3}\\ {0}& {-1}& {2}& {-1}\\ {0}& {2}& {1}& {5}\end{array}\right]\\ \text{•}& {}& \text{Multiply row 2 by -1; (R2 = -1*R2)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {2}& {0}& {3}\\ {0}& {1}& {-2}& {1}\\ {0}& {2}& {1}& {5}\end{array}\right]\\ \text{•}& {}& \text{Subtract 2 times row 2 from row 1; (R1 = R1-2*R2)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {0}& {4}& {1}\\ {0}& {1}& {-2}& {1}\\ {0}& {2}& {1}& {5}\end{array}\right]\\ \text{•}& {}& \text{Subtract 2 times row 2 from row 3; (R3 = R3-2*R2)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {0}& {4}& {1}\\ {0}& {1}& {-2}& {1}\\ {0}& {0}& {5}& {3}\end{array}\right]\\ \text{•}& {}& \text{Multiply row 3 by 1/5; (R3 = 1/5*R3)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {0}& {4}& {1}\\ {0}& {1}& {-2}& {1}\\ {0}& {0}& {1}& \frac{{3}}{{5}}\end{array}\right]\\ \text{•}& {}& \text{Subtract 4 times row 3 from row 1; (R1 = R1-4*R3)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {0}& {0}& {-}\frac{{7}}{{5}}\\ {0}& {1}& {-2}& {1}\\ {0}& {0}& {1}& \frac{{3}}{{5}}\end{array}\right]\\ \text{•}& {}& \text{Add 2 times row 3 to row 2; (R2 = 2*R3+R2)}\\ {}& {}& \left[\begin{array}{cccc}{1}& {0}& {0}& {-}\frac{{7}}{{5}}\\ {0}& {1}& {0}& \frac{{11}}{{5}}\\ {0}& {0}& {1}& \frac{{3}}{{5}}\end{array}\right]\end{array}$ (3)
 > $\mathrm{GaussJordanEliminationTutor}\left(M,v,\mathrm{output}=\mathrm{steps}\right)$
 $\begin{array}{lll}{}& {}& \text{Gauss-Jordan Solve}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {2}& {0}& {3}& {5}\\ {2}& {3}& {2}& {5}& {4}\\ {0}& {2}& {1}& {5}& {2}\end{array}\right]\\ \text{•}& {}& \text{Subtract 2 times row 1 from row 2; (R2 = R2-2*R1)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {2}& {0}& {3}& {5}\\ {0}& {-1}& {2}& {-1}& {-6}\\ {0}& {2}& {1}& {5}& {2}\end{array}\right]\\ \text{•}& {}& \text{Multiply row 2 by -1; (R2 = -1*R2)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {2}& {0}& {3}& {5}\\ {0}& {1}& {-2}& {1}& {6}\\ {0}& {2}& {1}& {5}& {2}\end{array}\right]\\ \text{•}& {}& \text{Subtract 2 times row 2 from row 1; (R1 = R1-2*R2)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {0}& {4}& {1}& {-7}\\ {0}& {1}& {-2}& {1}& {6}\\ {0}& {2}& {1}& {5}& {2}\end{array}\right]\\ \text{•}& {}& \text{Subtract 2 times row 2 from row 3; (R3 = R3-2*R2)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {0}& {4}& {1}& {-7}\\ {0}& {1}& {-2}& {1}& {6}\\ {0}& {0}& {5}& {3}& {-10}\end{array}\right]\\ \text{•}& {}& \text{Multiply row 3 by 1/5; (R3 = 1/5*R3)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {0}& {4}& {1}& {-7}\\ {0}& {1}& {-2}& {1}& {6}\\ {0}& {0}& {1}& \frac{{3}}{{5}}& {-2}\end{array}\right]\\ \text{•}& {}& \text{Subtract 4 times row 3 from row 1; (R1 = R1-4*R3)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {0}& {0}& {-}\frac{{7}}{{5}}& {1}\\ {0}& {1}& {-2}& {1}& {6}\\ {0}& {0}& {1}& \frac{{3}}{{5}}& {-2}\end{array}\right]\\ \text{•}& {}& \text{Add 2 times row 3 to row 2; (R2 = 2*R3+R2)}\\ {}& {}& \left[\begin{array}{ccccc}{1}& {0}& {0}& {-}\frac{{7}}{{5}}& {1}\\ {0}& {1}& {0}& \frac{{11}}{{5}}& {2}\\ {0}& {0}& {1}& \frac{{3}}{{5}}& {-2}\end{array}\right]\end{array}$ (4)