System Consistency
The consistency of a system of linear equations by ranks and its general solution, by the Rouché–Capelli theorem.
Each row holds the coefficients of the variables, then the constant term: x + 2y = 5 is written as 1 2 5. Up to 6 equations and 5 variables.
This calculator checks the consistency of a system of linear equations by ranks and writes its general solution.
The Rouché–Capelli theorem
- rank A ≠ rank (A|b): no solutions.
- rank A = rank (A|b) = n: a unique solution.
- rank A = rank (A|b) < n: infinitely many solutions.
Example. The system x + y = 1, 2x + 2y = 3 is inconsistent: rank A = 1, rank (A|b) = 2.
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