Let A ∈ Rm×n and b ∈ Rm, and let x0 be a particular solution of the system Ax = b. Prove the following:
(a) A vector y in Rn will be a solution of Ax = b if and only if y = x0 + z, where z ∈ N(A).
(b) If N(A) = {0}, then the solution x0 is unique.
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