Solve linear system Ax=b API

Solve a square linear system A·x = b via Cramer's rule (2x2/3x3) or Gaussian elimination with partial pivoting (NxN), detecting singular systems. Answers 'what x satisfies these simultaneous equations?'.

Price$0.03per request

MethodPOST

Route/v1/geometry/solve-linear-system

StatusLive

MIME typeapplication/json

Rate limit120/minute

Cache0s public

linear-systemcramergaussiansolveequationsmatrixlinear-algebra

API URLhttps://x402.hexl.dev/v1/geometry/solve-linear-system

Integration docs

Example request

{
  "a": [
    [
      2,
      1
    ],
    [
      1,
      3
    ]
  ],
  "b": [
    3,
    5
  ]
}

Example response

{
  "solution": [
    0.8,
    1.4
  ],
  "determinant": 5,
  "method": "Cramer's rule"
}

Input schema

{
  "type": "object",
  "required": [
    "a",
    "b"
  ],
  "properties": {
    "a": {
      "type": "array",
      "items": {
        "type": "array",
        "items": {
          "type": "number"
        }
      },
      "examples": [
        [
          [
            2,
            1
          ],
          [
            1,
            3
          ]
        ]
      ]
    },
    "b": {
      "type": "array",
      "items": {
        "type": "number"
      },
      "examples": [
        [
          3,
          5
        ]
      ]
    }
  }
}

Output schema

{
  "type": "object",
  "additionalProperties": true
}