Rref Calculator
RREF and Gauss-Jordan Calculator works out Reduced matrix and Rank from Matrix, Form and Last column is the constants (augmented system). The default figures on this page give reduced matrix of 1 0 0 2; 0 1 0 3; 0 0 1 -1; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
9 steps
- Starting 3x4 matrix:
- [ 2 1 -1 8 ]
- [ -3 -1 2 -11 ]
- [ -2 1 2 -3 ]
- Gauss-Jordan elimination: scale each pivot row to a leading 1 and clear the entries above and below it.
- [ 1 0 0 2 ]
- [ 0 1 0 3 ]
- [ 0 0 1 -1 ]
- Rank 3, nullity 1 (rank + nullity = 4 columns).
Reduced matrixtable
| 0 | 1 | 2 | 3 |
|---|---|---|---|
| 1 | 0 | 0 | 2 |
| 0 | 1 | 0 | 3 |
| 0 | 0 | 1 | -1 |
Its 4 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the RREF and Gauss-Jordan Calculator calculates
Row reduces a matrix to reduced row echelon or row echelon form, reporting rank, nullity, pivot and free columns, a null space basis, and the solution set when the matrix is augmented.
How to use this RREF and Gauss-Jordan Calculator
Enter Matrix, Form, Last column is the constants (augmented system) and Decimals shown. Reduced matrix updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Reduced matrix, Rank and Nullity.
The method follows Gilbert Strang, Introduction to Linear Algebra, ch. 3 (the four subspaces, rank, RREF) and Wikipedia, Row echelon form and Gaussian elimination.
Gauss-Jordan on a 3x3 system example
With Matrix: 2 1 -1 8; -3 -1 2 -11; -2 1 2 -3, Last column is the constants (augmented system): true, the calculator returns Reduced matrix: 1 0 0 2; 0 1 0 3; 0 0 1 -1, Rank: 3, Solution: x1 = 2; x2 = 3; x3 = -1. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Reduced matrix, Rank and Nullity. The inputs you can vary are Matrix, Form, Last column is the constants (augmented system) and Decimals shown.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
Can you do Rref on a calculator?
Row reduces a matrix to reduced row echelon or row echelon form, reporting rank, nullity, pivot and free columns, a null space basis, and the solution set when the matrix is augmented. Put your own figures in above and the working updates beside the result. For scale, the default figures on this page give 1 0 0 2; 0 1 0 3; 0 0 1 -1.
How to calculate Rref?
Row reduces a matrix to reduced row echelon or row echelon form, reporting rank, nullity, pivot and free columns, a null space basis, and the solution set when the matrix is augmented. Open “How this is worked out” beside the result to see each step for your own figures.
How to do Rref on a TI-84?
It needs Matrix, Form, Last column is the constants (augmented system) and Decimals shown. Nothing else is required, and the figures stay in your browser.
Is Rref only 1 and 0?
The result gives Reduced matrix, Rank, Nullity, Rows, Columns and Pivot columns, each labelled with its unit so the figure can be read on its own.
What information do I need for the RREF and Gauss-Jordan Calculator?
You need Matrix, Form, Last column is the constants (augmented system) and Decimals shown. The page opens with default figures that give reduced matrix of 1 0 0 2; 0 1 0 3; 0 0 1 -1, so you can see the scale before entering your own.
What does this RREF and Gauss-Jordan Calculator show?
It shows Reduced matrix, Rank, Nullity, Rows, Columns, Pivot columns, Free columns and System is consistent, with the working and any warnings for your entries.