MatrixCore.io Linear Systems Engine
Rational Math Active
Simultaneous Linear Solver

Gauss-Jordan Elimination Calculator

Solve systems of simultaneous linear equations with exact rational fractions and complex numbers. Capable of finding unique solutions, parameterizing infinitely many solutions with free variables, and checking system consistency.

Algorithm Principles
  1. Transform linear equations into an augmented matrix $[A \mid b]$.
  2. Eliminate elements above and below pivots to achieve Reduced Row Echelon Form (RREF).
  3. Detect inconsistencies: if any row yields $0 = k$ ($k \neq 0$), the system has no solution.
Quick Problem Presets
Matrix Dimension:
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