I understood that two systems of linear equations are equivalent if one can be obtained by the linear combination of the other system and vice versa. But can those two systems of equations be equivalent even if the solution $x_i=0? (1\le i\le n) $.Example set :
$ x_1-x_2=0 ;$
$ 2x_1+x_2=0 $
$ 3x_1+x_2=0 ;$
$ x_1+x_2=0 $
I got only zero as solution for both $x_1$ and $x_2$. Are these systems of equations equivalent?