Consider a matrixa∈ mm, nand a vectorb∈rm, and letax=bbe the correspondingsystem of linear equations. the systemax=0is then called thehomogeneous systemassociated toax=b. letsbe the set of solutions ofax=b, and lets0be the setof solutions of the associated homogeneous system. prove that ifx∈ sandu∈ s0thenx+u∈s.