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Discussion of a linear system


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.

Example:

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.

Example:

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.

Example:

As D = 0 and Dx0, the system is impossible and has no solution.

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