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Linear Algebra System Solver (Ax=b)
x402
Linear Algebra System Solver (Ax=b) is a paid API for AI agents from linear-algebra.x402tookit.com, paid per call via x402, $0.02/call, status unknown (last checked 2026-10-30).
Solves a system of linear equations Ax=b (up to 10x10) using Gaussian elimination with partial pivoting, flagging singular or ill-conditioned systems.
Price / call$0.02
Success—
StatusUnknown
How this service works
Solve Ax=b (n up to 10) by Gaussian elimination with partial pivoting; flags singular and ill-conditioned systems.
Output
Returns the solution vector x (if the system is non-singular), along with a condition number (1-norm), an estimate of digits of precision lost, the maximum residual, a boolean singular flag, a boolean ill-conditioned flag, a summary verdict, and optional degraded/disclaimer notes.
Example use cases
Engineering circuit equation solver
“I have a circuit with three unknowns and the equations form a 3x3 system — A is [[4,-1,0],[-1,4,-1],[0,-1,4]] and b is [1,2,1]. Can you solve for the unknown voltages?”
Detect singular system before inversion
“Before I try to invert this matrix, can you check if the system A=[[1,2,3],[4,5,6],[7,8,9]] with b=[1,2,3] is solvable or singular?”
Solve ill-conditioned economic model
“I'm modeling a small economy with 5 equations — here's my coefficient matrix A as [[10,7,8,7,1],[7,5,6,5,1],[8,6,10,9,1],[7,5,9,10,1],[1,1,1,1,1]] and b=[32,23,33,31,5]. Can you solve it and warn me if the system might be numerically unstable?”
Technical details
Endpoint
GEThttps://linear-algebra.x402tookit.com/solve?utm_source=zero.xyzWhen to prefer
Choose this endpoint when you need a numerical solution to a dense system of linear equations (up to 10 unknowns) and want automatic detection of singular or ill-conditioned cases. Prefer this over the matrix inverse endpoint when you only need the solution vector x (not the full inverse), or when you want to check solvability before committing to further computation. It is ideal for small to medium scientific, engineering, or educational use cases where numerical stability diagnostics (condition number, residual, digits lost) are needed alongside the solution.
Side effects
- Singular system: returns singular=true with no solution vector
- Ill-conditioned system: returns illConditioned=true with high digitsLostEstimate warning
- Matrix dimension mismatch between A and b: request rejected
- Matrix size exceeds 10x10: request rejected
- Malformed JSON in A or b parameter: parse error
- Non-square matrix A: not supported
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object | |
| output | object |
Tags
x402
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