# Sindri Linear Equation Solver

> Sindri Linear Equation Solver is a paid API for AI agents from x402.outpimp.com, paid per call via x402, $0.01/call, status unknown (last checked 2026-09-15).

Solves a system of linear equations (Ax = b) using LU decomposition for square coefficient matrices up to 20x20, with near-singularity detection.

## Facts

- Endpoint: POST https://x402.outpimp.com/solveLinearEquation
- Price: $0.01/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/sindri-linear-equation-solver-598242eb
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_RdL2NUpT_5kGLPeUfxmaQ

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability sindri-linear-equation-solver-598242eb -d '<json body>'
```

Example prompt: Can you solve this system of linear equations for me? The coefficient matrix is [[2,1,-1],[−3,−1,2],[−2,1,2]] and the right-hand side constants are [8,−11,−3].

## When to prefer this

Choose this endpoint when you need a fast, cheap ($0.01 USDC), server-side numerical solution to a dense square linear system up to 20×20. Ideal when you don't want to run a local numerical library, need LU decomposition specifically, or are building an agent that solves equations as part of a larger workflow. Not suitable for sparse systems, overdetermined/underdetermined systems, or systems larger than 20×20.

## Known failure modes

- Singular or near-singular matrix detected — system has no unique solution
- Matrix dimensions mismatch — coefficients array is not square or constants length doesn't match n
- Matrix exceeds 20x20 limit — request rejected
- Malformed input arrays — non-numeric values or missing fields cause 400 error
- Payment failure — x402 payment not processed, endpoint returns 402

## How this service works

Solves a system of linear equations (Ax = b) using the ml-matrix library's LU decomposition (LuDecomposition), with a near-singularity guard beyond the library's exact-singular check, for systems up to 20x20.

## Output

Returns the solution vector x (an array of n values) that satisfies Ax = b, where A is the input coefficient matrix and b is the constants vector. If the system is singular or near-singular, returns an error indicating the matrix cannot be solved.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "constants": {
   "type": "array",
   "description": "Array of n constants (the right-hand side of each equation)."
  },
  "coefficients": {
   "type": "array",
   "description": "Square 2D array of coefficients (n x n), up to 20x20."
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/sindri-linear-equation-solver-598242eb/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from x402.outpimp.com](https://www.zero.xyz/host/x402.outpimp.com/llms.txt)