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RREF.nb Mathematica notebook (current version)

RREF.pdf Mathematica notebook saved as PDF

1 Change history

1. Version July 17, 2023 of displayRREF. Add flag to turn on/off display of matrices
2. Version Oct 10, 2023 of displayRREF. Add flag so pivot not normalized to one and kept as is
3. Version Oct 14, 2023. Add displayREF which does forward elimination only
4. Version Oct 15, 2023. Fixed display again and improved row exchange
5. Version Dec 21, 2024. Fixed display of zering row statement. Code was correct, just display statement corrected
6. Version Feb 19, 2026. Fixed a bug where it missed a pivot if bottom row was all zeros. removed option to normalized pivot or not. Now it does normalization always.

2 Introduction and how to use

This describes how to use RREF.nb which contains one Mathematica function called displayRREF which displays on the screen all the steps in the forward Gaussian elimination process and also in the backward phase to produced a reduced row-echelon form when applied on a matrix \(A\). The matrix can be square or rectangular.

To use, download the RREF.nb from the link given at the top. Open the notebook using Mathematica, and evaluate the whole notebook using Evaluation->Evaluate Notebook. Now the function displayRREF is loaded and ready to be used.

Open a new notebook to use the function. Examples of usage are given below.

There are two functions in the notebook. displayRREF which does reduced RREF, and displayREF which does only the forward Gaussian elimination phase.

Any bugs please let me know.

Examples below shows how to use the functions

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