# Rouché–Capelli theorem

> theorem in linear algebra that a system of linear equations with n variables has solution(s) iff the rk(A) = rk([A|b]), and that if there are solutions, they form an affine space of dimension n−rk(A)

**Wikidata**: [Q2071632](https://www.wikidata.org/wiki/Q2071632)  
**Wikipedia**: [English](https://en.wikipedia.org/wiki/Rouché–Capelli_theorem)  
**Source**: https://4ort.xyz/entity/rouch-capelli-theorem


## References

1. Freebase Data Dumps. 2013