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Linear System Solver (Ax = b)
x402
Linear System Solver (Ax = b) is a paid API for AI agents from math-geometry.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-11-03).
Solves a system of linear equations Ax = b for up to 6 unknowns, returning the solution vector, rank, determinant, and classification (unique/none/infinite solutions).
Price / call$0.02
Success—
StatusUnknown
How this service works
Solve linear equations Ax = b (up to 6 unknowns): unique, none or infinite solutions, with rank and determinant.
Output
Returns a JSON object containing the solution vector (x1 through xN), rank of the coefficient matrix, determinant (for square systems), number of equations and unknowns, max residual for accuracy assessment, and a summary/verdict classifying the system as having a unique solution, no solution, or infinitely many solutions.
Example use cases
Engineering circuit analysis
“I have three loop equations from a circuit: coefficients are 4,1,-1;2,5,0;-1,2,3 and the voltage constants are 10,15,5. Solve for the three loop currents and tell me whether there's a unique solution.”
Economics input-output model
“Solve this 4-variable economic system for me: coefficient matrix is 1,-0.2,-0.3,0;-0.1,1,-0.2,-0.1;-0.2,-0.1,1,-0.2;-0.1,-0.1,-0.2,1 with demand constants 100,200,150,120. Give me the output levels and the rank of the matrix.”
Checking underdetermined geometry system
“I have the equations 1,2,3;4,5,6 with constants 6,15 — only 2 equations but 3 unknowns. Solve the system and tell me if there are infinite solutions or none.”
Technical details
Endpoint
GEThttps://math-geometry.x402tookit.com/linear-system?utm_source=zero.xyzWhen to prefer
Use this endpoint when you need to solve a concrete numerical system of linear equations (Ax = b) with up to 6 unknowns and want both the solution and diagnostic metadata (rank, determinant, solution classification). Prefer it over a general matrix operations endpoint when the goal is solving for unknowns rather than matrix transformations. It handles the underdetermined and overdetermined cases by reporting solution type rather than failing.
Side effects
- Malformed matrix string (wrong delimiter or non-numeric values) causes a parse error
- Matrix dimensions mismatch between matrix and constants returns an error
- System with more than 6 unknowns is not supported
- Singular matrix (determinant = 0) returns no-unique-solution verdict rather than a numeric answer
- Empty or missing query parameters return a 400-level error
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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