Theorem 1.5 is known as Rouche-Capelli Theorem in Italy, Kronecker-
Capelli Theorem in Russia, Rouche-Fontene Theorem in France, and Rouche-
Frobenius Theorem in Spain and many countries in Latin America. Eugene
Rouche (1832-1910) wrote the condition for consistency in 1875 in terms of
the existence of non-zero minors of same order in A and in the augmented
matrix [20].