{"uid":"cap_RdL2NUpT_5kGLPeUfxmaQ","slug":"sindri-linear-equation-solver-598242eb","name":"Sindri Linear Equation Solver","description":"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.","url":"https://x402.outpimp.com/solveLinearEquation","method":"POST","headers":{},"bodySchema":{"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."}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.01","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":"$0.01/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.01","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.01","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_Q-f6QrlbZvNSSabmUrb-x","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.01","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Solves a system of linear equations (Ax = b) using LU decomposition for square coefficient matrices up to 20x20, with near-singularity detection.","exampleAgentPrompt":"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].","exampleUseCases":[{"title":"Structural engineering load calculation","prompt":"I have a 3-equation structural load system. The coefficients are [[4,2,0],[2,3,1],[0,1,2]] and the right-hand side values are [10,14,8]. Can you solve for the unknown forces?"},{"title":"Economics supply-demand equilibrium","prompt":"Solve this 4-variable economic equilibrium system for me — coefficients are [[1,-1,0,0],[0,1,-1,0],[0,0,1,-1],[1,0,0,1]] and the constants vector is [5,3,2,10]."},{"title":"Circuit analysis with Kirchhoff's laws","prompt":"I've set up Kirchhoff's voltage law equations for my circuit as a 3x3 matrix [[10,-3,-2],[-3,8,-1],[-2,-1,6]] with constants [20,15,10] — can you find the unknown currents?"}],"resultDescription":"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.","failureModes":["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"],"whenToPreferThis":"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.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-09-15T12:51:11.104Z","isFirstParty":false}