Gaussian Elimination Calculator
Solve systems of linear equations using Gaussian elimination with step-by-step solution and augmented matrix display.
Published by:
isCalculator Editorial Team
Was this calculator helpful?
How to use this tool?
How to Use the Gaussian Elimination Calculator
This calculator solves a system of linear equations using Gaussian elimination with partial pivoting. Follow these steps:
- Set the number of equations (2 to 10) using the Number of Equations input. The matrix will update automatically.
- Enter the coefficients for each equation in the form:
a₁x₁ + a₂x₂ + ... + aₙxₙ = b. Fill in all coefficient fields and the constantbon the right. Use decimal numbers if needed (e.g.,3.5). - Click "Solve" to compute the solution.
Output:
- Solution shows the values of each variable (
x₁, x₂, ...) rounded to 4 decimal places. - Steps display the row operations performed (swaps and eliminations) for transparency.
Note: If the system has no unique solution (e.g., inconsistent or infinite solutions), the calculator will indicate "No solution" or set free variables to 0.
Previous Results
| Result | Inputs | Date |
|---|
Frequently Asked Questions
Gaussian elimination is a method to solve systems of linear equations by transforming the augmented matrix into row-echelon form using row operations, then back-substituting to find the solution.
You can solve systems with 2 to 10 equations. The calculator automatically adjusts the matrix size.
The calculator detects inconsistent systems (no solution) by identifying a row with all zeros in coefficients but non-zero constant. For infinite solutions, it sets free variables to zero and solves for the rest, but a warning is shown.
