Are homogenous systems of equations with a trivial solution always consistent?

If a homogeneous system of equations has only a trivial solution , can we call it consistent ?

For example , consider

$a_1x+b_1y+c_1z=0$

$a_2x+ b_2y +c_2z=0$

$a_3x+b_3y+c_3z=0$

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 ?

• Consistency is nothing more than the existence of at least one solution. The trivial solution is a solution, so any homogeneous system is necessarily consistent. – Sriram Gopalakrishnan Aug 1 '18 at 2:53
• Also your matrix of coefficients is row equivalent to identity matrix – Tutankhamun Aug 1 '18 at 2:59
• Thank you ! But I was confused whether (0,0,0) would classify for consistently since we call it trivial. But now I know the answer :) – Aditi Aug 1 '18 at 3:02