{"uid":"cap_Uti45uQ3GvtSiZCtsaAVk","slug":"exact-linear-system-solver-cb8875ce","name":"Exact Linear-System Solver","description":"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.","url":"https://www.mahastrategies.com/api/v1/compute/numerics/linear-system?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"rhs":{"type":"array","maxItems":8,"minItems":1},"matrix":{"type":"array","maxItems":8,"minItems":1},"dataClass":{"enum":["public","synthetic"],"type":"string"}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.011002","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.011002/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.011002","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.011002","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_lF_auOAui8V2jImKw-z4B","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.011002","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"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.","exampleAgentPrompt":"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.","exampleUseCases":[{"title":"Verify unique solution in robotics calibration","prompt":"I have a 3-variable linear system from my calibration equations: matrix [[1,2,0],[0,1,3],[2,0,1]] with right-hand side [5,4,3], marked as synthetic data. Solve it exactly and tell me whether there's a unique solution, what the rank is, and list the pivot columns."},{"title":"Detect underdetermined system in resource allocation","prompt":"Can you solve this underdetermined linear system exactly? The matrix is [[1,1,1],[2,2,2]] and the right-hand side is [6,12] — data class is synthetic. I need to know the particular solution, the full null space basis, and whether the system has infinitely many solutions."},{"title":"Identify inconsistent system in constraint checking","prompt":"Check whether this 4-variable linear system is consistent: matrix [[1,0,1,0],[0,1,0,1],[1,1,1,1],[2,2,2,2]] with right-hand side [3,4,6,15], public data. Give me the exact rank, pivots, and confirm if it has no solution."}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-10-15T06:39:11.999Z","isFirstParty":false,"canonicalSlug":"exact-linear-system-solver-cb8875ce"}