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Matrix Linear System Solver (Ax=b)
x402
Matrix Linear System Solver (Ax=b) is a paid API for AI agents from matrix.openverbs.com, paid per call via x402, $0.004/call, status unknown (last checked 2026-09-15).
Solves a square linear system A·x = b using Gaussian elimination with partial pivoting, returning the solution vector or a solvable:false flag for singular systems.
Price / call$0.004
Success—
StatusUnknown
How this service works
Solve the linear system A·x = b for a square coefficient matrix A and vector b via Gaussian elimination with partial pivoting. A non-square A or a b of the wrong length is a clean 400. A singular system is NOT an error — it returns a successful { solvable:false, solution:null }.
Output
Returns a JSON object with a boolean 'solvable' field and a 'solution' field containing the solution vector x (array of floats) if solvable, or null if the system is singular. Non-square A or mismatched b length returns a 400 error.
Example use cases
Structural engineering load distribution
“I need to find the force distribution in a 4-member truss — the stiffness matrix A is [[10,−2,0,0],[−2,8,−3,0],[0,−3,9,−4],[0,0,−4,6]] and the load vector b is [100,0,50,0]. Can you solve it?”
Check if underdetermined system is singular
“I have a 3×3 coefficient matrix A = [[1,2,3],[4,5,6],[7,8,9]] and b = [6,15,24]. Is this system actually solvable or is the matrix singular?”
Economics input-output model equilibrium
“I'm modeling an input-output economy with technology matrix A = [[0.1,0.3],[0.4,0.2]] and demand vector b = [50,30]. Solve for the production levels x.”
Technical details
Endpoint
POSThttps://matrix.openverbs.com/v1/solveWhen to prefer
Use this endpoint when you need to numerically solve a square linear system Ax=b and want clean handling of singular systems (returns solvable:false rather than throwing). Prefer this over matrix inversion when you only need the solution vector x, not the inverse of A itself. Best for well-defined square systems; does not support least-squares or overdetermined systems.
Side effects
- 400 if matrix A is not square
- 400 if length of b does not match the dimension of A
- 400 if the matrix is ragged (rows of unequal length)
- 400 if A or b are empty
- Singular system returns {solvable:false, solution:null} rather than an error
- Floating-point precision issues for near-singular systems may affect accuracy
Input
Schema · Request body
| Field | Type | Description |
|---|---|---|
| inputrequired | object |
Tags
x402
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