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would you please go over my explanations why each set of elements is or is not vector space. (see attachment). Also Please show the proof

would you please go over my explanations why each set of elements is or is not vector space. (see attachment). Also Please show the proof for questions #12. I think #3,4,10.11 are similar to 12 as they involved inhomogeneous equation. Much appreciated help in proving vector space.

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