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.
algebra-precalculuslinear algebraterminologytrigonometry
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.
Best Answer
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.