GaussJordanEliminationTutor - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim

Home : Support : Online Help : Education : Student Packages : Linear Algebra : Interactive : GaussJordanEliminationTutor

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

Calling Sequence

GaussJordanEliminationTutor(M, opts)

GaussJordanEliminationTutor(M, v, opts)










(optional) equation(s) of the form option=value where equation is output or displaystyle



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 <M | v> 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.












Gauss-Jordan Reduce120323250215 Subtract 2 times row 1 from row 2; (R2 = R2-2*R1)12030−12−10215 Multiply row 2 by -1; (R2 = -1*R2)120301−210215 Subtract 2 times row 2 from row 1; (R1 = R1-2*R2)104101−210215 Subtract 2 times row 2 from row 3; (R3 = R3-2*R2)104101−210053 Multiply row 3 by 1/5; (R3 = 1/5*R3)104101−2100135 Subtract 4 times row 3 from row 1; (R1 = R1-4*R3)1007501−2100135 Add 2 times row 3 to row 2; (R2 = 2*R3+R2)1007501011500135



Gauss-Jordan Solve120352325402152 Subtract 2 times row 1 from row 2; (R2 = R2-2*R1)120350−12−1−602152 Multiply row 2 by -1; (R2 = -1*R2)1203501−21602152 Subtract 2 times row 2 from row 1; (R1 = R1-2*R2)1041−701−21602152 Subtract 2 times row 2 from row 3; (R3 = R3-2*R2)1041−701−2160053−10 Multiply row 3 by 1/5; (R3 = 1/5*R3)1041−701−21600135−2 Subtract 4 times row 3 from row 1; (R1 = R1-4*R3)10075101−21600135−2 Add 2 times row 3 to row 2; (R2 = 2*R3+R2)100751010115200135−2Extract equations from the matrixx17x45=1x2+11x45=2x3+3x45=−2Introduce free variablesx4=tx17t5=1x2+11t5=2x3+3t5=−2Solutionx1=1+7t5x2=211t5x3=23t5x4=t


See Also

Student[LinearAlgebra], Student[LinearAlgebra][AddRow], Student[LinearAlgebra][GaussianElimination], Student[LinearAlgebra][GaussianEliminationTutor], Student[LinearAlgebra][LinearSolve], Student[LinearAlgebra][LinearSolveTutor], Student[LinearAlgebra][MultiplyRow], Student[LinearAlgebra][ReducedRowEchelonForm], Student[LinearAlgebra][SwapRow]