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Gauss-Jordan Linear System Solver — result sheet
Solve a small square system of linear equations from a coefficient matrix and right-hand-side vector using reduced row echelon elimination.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Apply elementary row operations to [A|b] until the left block is the identity matrix; the final augmented column is x = A⁻¹b when a unique solution exists.
Gauss-Jordan elimination makes pivot columns into identity columns. Partial pivoting improves numerical stability, while a zero pivot with a nonzero residual identifies an inconsistent system and a zero row identifies a non-unique system.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Coefficient matrix — Rows use semicolons; entries use commas. Use a square matrix from 2×2 through 4×4.
- Right-hand side — Enter one comma-separated value for each matrix row.
Worked example
| Input | Value |
|---|---|
| Coefficient matrix | 2, 1; 1, -1 |
| Right-hand side | 5, 1 |
x₁ = 2, x₂ = 1
Assumptions and limits
- The coefficient matrix is square with 2 to 4 rows and columns.
- All entries are real finite numbers and the solver reports only a unique finite solution.
- Near-zero pivots use a scale-aware tolerance; exact symbolic parameters are not supported.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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