Question: Suppose that x, y Cn, b Cm and A is an m n matrix. If x, y and x + y are

Suppose that x, y ∈ Cn, b ∈ Cm and A is an m × n matrix. If x, y and x + y are each a solution to the linear system LS(A, b), what interesting can you say about b? Form an implication with the existence of the three solutions as the hypothesis and an interesting statement about LS(A, b) as the conclusion, and then give a proof.

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