This problem outlines a proof that two linear systems LS₁ and LS₂ are equivalent (that is, have the same solution set) if their augmented coefficient matrices A₁ and A₂ are row equivalent.
(a) If a single elementary row operation transforms A₁ to A₂, show directly—considering separately the three cases—that every solution of LS₁ is also a solution of LS₂.

(b) Explain why it now follows from Problem 29 that every solution of either system is also a solution of the other system; thus the two systems have the same solution set.