Concept of Trial and Non Trivial

Nontrivial

A solution or example that is not trivial. Often, solutions or examples involving the number zero are considered trivial. Nonzero solutions or examples are considered nontrivial.

For example, the equation x + 5y = 0 has the trivial solution (0, 0). Nontrivial solutions include (5, - 1) and (-2, 0.4).

And the system of equation in which the determinant of the coefficient matrix is not zero but the solution are x=y=z=0 is called trivial solution.