If a linear system has no equations and no unknowns, it can be:
The) possible and determinedif D = det A0; in which case the solution is only.
m = n = 3
Then the system is possible and determined, having a unique solution.
B) possible and undeterminedif D = Dx1 = Dx2 = Dx3 =… = Dxn= 0, for n = 2. If n3, this condition is valid only if there are no equations with respectively proportional unknown coefficients and non-proportional independent terms. A possible and undetermined system has infinite solutions.
D = 0, Dx = 0, Dy= 0 and Dz=0
Thus the system is possible and undetermined, having infinite solutions.
ç) impossible, if D = 0 and Dxi0, 1 in; in which case the system has no solution.
As D = 0 and Dx0, the system is impossible and has no solution.Next: Equivalent Systems