# Two homogenous system are equivalent if they have the same answer

Prove that two homogeneous systems of linear equations are equivalent iff they have the same solution set.

My definition of equivalent of linear equations is that each equation of system AA is a linear combination of the equations of system BB and converse.

So i have a bit trouble proving this statement in general as m×nm\times n form. I worked with their coefficient matrices and if i show that these two are row equivalent the problem is solved. Is there any method to use for this? If not what’s the general prove.

=================

=================

=================