What rrefcalculator.io offers
rrefcalculator.io is a free, independent website for one job in linear algebra: row-reducing a matrix and understanding the result. It has three parts.
- The RREF calculator reduces any matrix from 1×1 to 6×7 to reduced row echelon form or row echelon form, with exact fractions and every row operation shown.
- The augmented matrix calculator solves systems of linear equations, compares the rank of A with the rank of [A | b], and writes infinite solutions in free parameters.
- The guides explain how to find RREF by hand, how REF differs from RREF, and how to run the rref( command on a TI-83 Plus or TI-84 Plus.
No account is needed, there are no ads, and your matrices are calculated in your own browser. They are never sent to our server.
Who it is for
The site is written for students taking a first course in linear algebra or matrix methods, for anyone checking homework or revision by hand, and for instructors who want a quick, exact check of a worked example. The guides assume you know what a matrix is, but not how row reduction works.
How the calculator produces its answers
The calculator never uses floating-point numbers for elimination. Every entry is converted to an exact fraction, and every row operation is carried out in exact rational arithmetic. Decimals are only a display option and are rounded to 8 significant digits; the copied matrix stays exact.
Before each release, the calculation engine is checked automatically against:
- hand-verified examples covering unique, infinite and inconsistent systems, row swaps, zero matrices, tall and wide matrices, fractions and decimals;
- 120 generated matrices, each checked against the defining properties of reduced row echelon form;
- a replay of every listed row operation, confirming that each step produces exactly the matrix shown;
- invalid input such as blank cells, zero denominators, symbols and numbers that are too long.
If any check fails, the site is not published.
How the guides are written and reviewed
Every matrix in a guide is computed by the same engine the calculator uses when the site is built, and the build stops if an example no longer matches its explanation. Definitions and hardware instructions are checked against primary sources, which are named at the end of each guide:
- University of Texas at Austin, Matrix Operations appendix, for row operations, echelon forms, rank and solution types;
- Texas Instruments, support solution 34713, for the TI-83 Plus and TI-84 Plus key sequences.
Each guide shows the date it was last updated. The worked examples are original; no screenshots or text are copied from other sites or textbooks.
Editorial principles
Accuracy over reach
We only publish a calculator feature once its mathematics has been implemented and tested. Symbolic coefficients, complex numbers, arithmetic over GF(2), matrix inverses and vector-form solutions are not supported yet, and the site says so rather than approximating them.
Show the working
An answer without its steps is hard to learn from, so every result lists the row operations that produced it.
Honest limits
We do not publish invented reviews, ratings, statistics, credentials or testimonials. When something has not been verified, such as behaviour on calculator models we have not checked against an official source, we say so.
Independence
rrefcalculator.io is not affiliated with, sponsored by or endorsed by Texas Instruments, any university or any other calculator provider. It carries no advertising, affiliate links or sponsored content.
Corrections and feedback
If you find a result, step or explanation that looks wrong, please tell us through the contact form and choose “Report a calculation problem”. Include the matrix you entered. Confirmed errors are corrected, and the page's update date changes when its content changes.
Who runs the site
rrefcalculator.io is an independent website. Content is published under the site's name rather than an individual byline. You can reach the operator through the contact page. How we handle personal data is described in the privacy policy.