Row Echelon Calculator
Convert any matrix to Row Echelon Form (REF) using Gaussian elimination. Supports 2x2, 3x3, and 4x4 matrices.
Published by:
isCalculator Editorial Team
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How to use this tool?
This calculator transforms a square matrix into its Row Echelon Form (REF) using Gaussian elimination.
- Select Matrix Size – Choose 2×2, 3×3, or 4×4 from the dropdown.
- Enter Values – Fill each cell with a number (decimals allowed). Empty cells default to 0.
- Click "Calculate REF" – The result shows the row echelon matrix and each step performed.
Output: The matrix is displayed with values rounded to 4 decimal places. Steps show row swaps, divisions, and subtractions.
Tip: All inputs are numeric. Use a dot (.) for decimals. No special formatting required.
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Frequently Asked Questions
Row Echelon Form (REF) is a matrix form where each nonzero row has a leading 1, and the leading 1 in a row is to the right of the leading 1 in the row above. All rows consisting entirely of zeros are at the bottom.
It performs Gaussian elimination: swapping rows, scaling rows, and adding multiples of rows to eliminate entries below the pivot.
The calculator supports 2x2, 3x3, and 4x4 matrices. Select the size from the dropdown.
