# Exact Linear-System Solver

> Exact Linear-System Solver is a paid API for AI agents from www.mahastrategies.com, paid per call via x402, $0.011002/call, status unknown (last checked 2026-10-15).

Solves a 1–8 variable rational linear system exactly, returning rank, pivot positions, particular solution, and null space with classification of unique, inconsistent, or underdetermined systems.

## Facts

- Endpoint: POST https://www.mahastrategies.com/api/v1/compute/numerics/linear-system?utm_source=zero.xyz
- Price: $0.011002/call
- Payment: x402
- Status: unknown
- Last checked: 2026-10-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/exact-linear-system-solver-cb8875ce
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_Uti45uQ3GvtSiZCtsaAVk

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 exact-linear-system-solver-cb8875ce -d '<json body>'
```

Example prompt: Solve this linear system exactly — matrix [[2,1],[5,3]] with right-hand side [4,7], treating it as synthetic data — and tell me whether it has a unique solution, and if so what it is along with the rank and pivots.

## When to prefer this

Choose this endpoint when you need provably exact solutions to small rational linear systems (up to 8 variables) and cannot tolerate floating-point conditioning errors. It is ideal for verification, symbolic reasoning, constraint satisfaction checks, and audit scenarios where the exact rank, pivot structure, and null space must be inspectable and reproducible. Prefer alternatives for larger systems, systems with floating-point or approximate coefficients, or when physical-model interpretation is required.

## Known failure modes

- Matrix or RHS dimensions mismatch (rows of matrix must equal length of RHS)
- Matrix exceeds 8×8 limit — request rejected
- Invalid dataClass value outside enum ['public','synthetic']
- Malformed JSON input returns 400 error
- Payment not settled via x402 protocol returns 402 Payment Required
- System with non-rational entries may cause parse errors

## How this service works

Get an inspectable exact solution to a 1-8 variable rational linear system. Returns rank, pivots, particular solution and null space; distinguishes unique, inconsistent and underdetermined systems. No floating-point conditioning or physical-model assessment. New modular adapter: retained result recovery for 24 hours, minimal receipt metadata for 90 days. Existing live route unchanged.

## Output

Returns the rank of the coefficient matrix, the pivot column indices, a particular solution vector (if the system is consistent), a basis for the null space (for underdetermined systems), and a classification label indicating whether the system has a unique solution, is inconsistent, or is underdetermined. Results are exact rational arithmetic — no floating-point rounding. Retained results are recoverable for 24 hours; minimal receipt metadata is kept for 90 days.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "rhs": {
   "type": "array",
   "maxItems": 8,
   "minItems": 1
  },
  "matrix": {
   "type": "array",
   "maxItems": 8,
   "minItems": 1
  },
  "dataClass": {
   "enum": [
    "public",
    "synthetic"
   ],
   "type": "string"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/exact-linear-system-solver-cb8875ce/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from www.mahastrategies.com](https://www.zero.xyz/host/www.mahastrategies.com/llms.txt)