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Gaussian-elimination solution for small Ax = b systems with determinant and residual table.
Linear System Solver is a browser-local ScholarTool numerical-method calculator. Enter the required expression, table, or matrix values, then click Solve Linear System; default values and edits do not publish a final result until that explicit action succeeds.
Configure inputs first. Results, visuals, downloads, and copy summary remain hidden until Solve Linear System succeeds.
Expressions use a restricted math parser and run in the browser. The tool accepts finite real-number inputs only and does not execute arbitrary code.
The Linear System Solver parses a coefficient matrix and right-hand-side vector, applies partial-pivot Gaussian elimination, and reports solution components with residual checks.
The calculator reports the main estimate first, then shows iteration history, intermediate sample values, residual checks, warnings, and a result-driven visual. Outputs are intended for education, estimation, assignment checking, and preliminary engineering computation workflows, not final certification.
Inputs are processed locally in the browser with deterministic TypeScript logic. Expression tools use the restricted ScholarTool math parser, which accepts ordinary mathematical syntax but does not execute scripts or arbitrary code.
Gaussian elimination transforms the coefficient matrix into upper-triangular form with partial pivoting, then uses back substitution to compute the solution vector.
A x = bA is the coefficient matrix, x is the unknown vector, and b is the right-hand side.
r = A x - bResiduals check how closely the solution satisfies the original equations.
| Symbol | Meaning | Unit |
|---|---|---|
| A | Coefficient matrix | problem units |
| x | Unknown solution vector | varies |
| b | Right-hand-side vector | varies |
| r | Residual vector | same as b |
This numerical-method tool is intended for educational, estimation, and preliminary engineering or research use. Always verify critical numerical results with analytical checks where possible, validated software, applicable standards, measured data, and qualified professional judgment before using results in real design, manufacturing, construction, safety, research, or compliance decisions.
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Visit ScholarEaseLast reviewed: 2026-07-08