Rouché–Capelli theorem
Rouché–Capelli theorem is a theorem in linear algebra that determines the number of solutions of a system of linear equations, given the ranks of its augmented matrix and coefficient matrix. The theorem is variously known as the: Rouché–Capelli theorem in English speaking countries, Italy and Brazil; Kronecker–Capelli theorem in Austria, Poland, Ukraine, Bosnia, Croatia, Romania, Serbia and Russia; Rouché–Fontené theorem in France; Rouché–Frobenius theorem in Spain and many countries in Latin America; Frobenius theorem in Czechia and Slovakia.