Gauss Jordan Elimination Calculator
Solve systems of linear equations using the Gauss-Jordan elimination method. Input a square matrix and its constants to get the reduced row echelon form and solution.
Published by:
isCalculator Editorial Team
Was this calculator helpful?
How to use this tool?
This calculator solves a system of n linear equations with n unknowns using the Gauss-Jordan elimination method. It transforms the augmented matrix into Reduced Row Echelon Form (RREF) and displays the solution step-by-step.
- Set Matrix Size: Enter a number between 2 and 6 in the Matrix Size field. The grid updates automatically.
- Enter Coefficients: Fill in the aij boxes (coefficients of variables) and the bi boxes (constants on the right side of each equation). Use decimal numbers if needed.
- Calculate: Click the Calculate button. The result shows:
- The final RREF matrix (with the solution column after the vertical bar).
- The values of each variable (x1, x2, ..., xn).
- A step-by-step log of row operations performed.
- Error Handling: If the matrix is singular (no unique solution) or any field is empty/invalid, an error message appears. Correct the inputs and try again.
Tip: All numbers are displayed with 4 decimal places. The calculator uses partial pivoting for numerical stability.
Previous Results
| Result | Inputs | Date |
|---|
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 row operations.
This calculator supports square matrices from 2x2 up to 6x6.
If the matrix is singular (determinant zero), the system may have no solution or infinitely many solutions. The calculator will indicate singularity.
