Question: (a) Can you construct an example of a subset S R2 with the property that eve S for any c R, v

(a) Can you construct an example of a subset S ⊂ R2 with the property that eve S for any c ∈ R, v ∈ S, and yet S is not a subspace?
(b) What about an example where v + w ∈ S for every v, w ∈ S, and yet S is not a subspace?

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