What does it mean for a system of equations to have a non trivial solution? What does it mean for a system of equations to have a non trivial solution?
Trivial means obviously but how can a equation have a obvious solution?
My book says if solution is  non trivial than determinant of coefficient of variables is 0.


The word is often used about systems of equations such as
$$ 3x+5y-12z = 0 \\ x-y+5z = 0 \\ 5x+y+3z=0 $$
where it is immediately obvious that setting all of the unknowns to $0$ will solve the system. The question is then whether the system has other solutions than that.
