This problem outlines a proof that two linear systems LS 1 and LS 2 are equivalent (that is, have the same solution set) if their augmented coefficient matrices A 1 and A 2 are row equivalent (a) If a single elementary row operation transforms A 1 to A 2 , show directlyconsidering separately the three casesthat every solution of LS 1 is also a solution of LS 2 (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

Question: This problem outlines a proof that two linear systems LS 1 and LS 2 are equivalent (that is, have the same solution set) if their

This problem outlines a proof that two linear systems LS₁and 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.

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