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)
Kronecker-Capelli theorem; Rouché-Frobenius theorem; Rouché-Capelli theorem; Rouche–Capelli theorem; Rouche-Capelli theorem
In linear algebra, the Rouché–Capelli theorem determines the number of solutions for a system of linear equations, given the rank of its augmented matrix and coefficient matrix. The theorem is variously known as the: