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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{LinearAlgebra}\right]\right)\&colon;$

$M≔⟨⟨1\&comma;2\&comma;0⟩\left|⟨2\&comma;3\&comma;2⟩\right|⟨0\&comma;2\&comma;1⟩|⟨3\&comma;5\&comma;5⟩⟩$

$M≔\left[\begin{array}{cccc}1& 2& 0& 3\\ 2& 3& 2& 5\\ 0& 2& 1& 5\end{array}\right]$

$v≔⟨5\&comma;4\&comma;2⟩$

$v≔\left[\begin{array}{c}5\\ 4\\ 2\end{array}\right]$

$\mathrm{GaussJordanEliminationTutor}\left(M\right)$

$\mathrm{GaussJordanEliminationTutor}\left(M\&comma;v\right)$