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.

Remember that if u is a solution of the linear system Ax=b then satisfies that Au=b. Then, since , , and since then .

Now we need show that A(x+u)=b. Observe that , this implies that

h df tyjgtyj ttd y ytkgfty ty

step-by-step explanation:

tyty jry j y yj yttj yhgtyj y ghyj ytthj

i dont know sorry

step-by-step explanation: