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Question: linear algebra...

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Linear algebra:

1 Prove or disprove that the following sets are (sub-)vector spaces. Note: If your vector spaces are already contained in a well-known vector space such as Rn, C0(R), it suffices to show that the spaces are closed or not closed under the addition and the scalar multiplication because it guarantees the associative laws, commutative laws etc., once the addition and the scalar multiplication are well-defined on your spaces.

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