Question: Let A Rmn, b Rm, and let x0 be a particular solution to the system Ax = b. Prove the following. A vector

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

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