Row Echelon Form Calculator
Transform any matrix into row echelon form (REF) using Gaussian elimination. Supports up to 4x4 matrices with step-by-step explanation.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Row Echelon Form Calculator
- Set matrix dimensions: Enter the number of Rows (1–4) and Columns (1–4) using the input fields.
- Enter matrix values: Fill each cell with a number (decimals allowed). All cells must contain valid numbers.
- Compute REF: Click the Compute REF button.
- Read the results:
- The Row Echelon Form table shows the transformed matrix with leading 1s (pivots) and zeros below them.
- The Steps section lists each operation performed (row swaps, scaling, elimination).
Note: All values are displayed with 4 decimal places. Numbers very close to zero are shown as 0.
Previous Results
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Frequently Asked Questions
Row echelon form (REF) is a matrix form where all nonzero rows are above rows of all zeros, and the leading coefficient of a nonzero row is always to the right of the leading coefficient of the row above it.
It performs Gaussian elimination: it finds pivots, swaps rows if needed, scales rows to make pivots 1, and eliminates entries below pivots.
You can compute REF for matrices from 1x1 up to 4x4.
