Gaussian Elimination Calculator
Solve a square linear system by scaled pivot elimination and inspect its reduced augmented matrix and residual.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Enter one augmented row for each unknown. Choose a scaled pivot and normalize its row. Eliminate that column from every other row. Read the solution or rank classification and check residuals.
Augmented matrix [A|b] → reduced row-echelon form
Worked example
The system x+y+z=6, 2x−y+z=3, x+2y−z=2 has solution x=1, y=2, z=3.
Assumptions and input details
Two to six equations with the same number of unknowns. Coefficient magnitudes are at most one billion. Calculations use floating-point arithmetic; systems that are numerically too ill-conditioned are rejected rather than assigned a reliable solution.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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