x = y = z = 0 is trivial solution, and [A] = 0 is non-trivial solution. The determinant of the coefficients of x,y,z must be equal to zero for the existence of non trivial solution. For example, the trivial solution of the equation x+5y=0 is x=0,y=0. And non-trivial solutions are x=5,y=–1 and x=–2,y=0.4. Often, solutions involving the number zero are considered trivial. Thus, nonzero solutions are considered nontrivial.