If a homogeneous system of equations has only a trivial solution , can we call it consistent ?
For example , consider
$a_2x+ b_2y +c_2z=0$
Regardless of the values of the coefficents, $(0,0,0)$ will always be a solution of the above system of equations. Now we make an assumption that the system has only a trivial solution. Would we call these equations consistent in that case ?