Gauss Jordan Calculator
Solve systems of linear equations using the Gauss-Jordan elimination method. Enter the augmented matrix and get the reduced row echelon form step by step.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Gauss-Jordan Elimination Calculator
- Set Matrix Size: Enter the number of rows (equations, 2–6) and columns (variables + constants, 2–7). The last column is for constants (the right-hand side).
- Generate Matrix: Click "Generate Matrix" to create input fields.
- Enter Values: Fill all cells with numbers (decimals allowed). Placeholders show a for coefficients and b for constants.
- Solve: Click "Solve" to compute the Reduced Row Echelon Form (RREF).
- Read Results: The RREF matrix appears above, with a vertical bar separating coefficients from constants. Below, each step (row swaps, scaling, elimination) is listed.
Tip: Use decimal numbers (e.g., 0.5) or fractions like 1/3 (the calculator converts to decimals). All values are rounded to 4 decimal places in output.
Previous Results
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Frequently Asked Questions
Gauss-Jordan elimination is an algorithm to solve systems of linear equations by transforming the augmented matrix into reduced row echelon form (RREF) using elementary row operations.
Set the number of rows (equations) and columns (variables + constants), click 'Generate Matrix', fill in the coefficients and constants, then click 'Solve' to see the RREF and steps.
If the RREF contains a row of zeros except a non-zero constant, the system is inconsistent and has no solution. The calculator will still show the RREF matrix.
