If a linear system has **no** equations and **no** unknowns, it can be:

The) **possible and determined**if D = det A0; in which case the solution is *only.*

Example:

m = n = 3

Then the system is possible and determined, having a unique solution.

B) **possible and undetermined**if D = D_{x1 }= D_{x2} = D_{x3} =… = D_{xn}= 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.

Example:

D = 0, D_{x }= 0, D_{y}= 0 and D_{z}=0

Thus the system is possible and undetermined, having infinite solutions.

ç) **impossible**, if D = 0 and D_{xi}0, 1 in; in which case the system has no solution.

Example:

As D = 0 and D_{x}0, the system is impossible and has no solution.