**Unformatted text preview: **explicitly demonstrates that the set does not satisfy the deﬁnition of a subspace. 3.2: 1b, 1c, 2a, 2c, 3d, 3f, 5b, 5c, 6d, 6e (2) 3.2.20. Prove the statement for a generic vector space W by verifying that U ∩ V satisﬁes the deﬁnition of a subspace. (3) 3.2.22. Prove the statement for a generic vector space W by verifying that U + V satisﬁes the deﬁnition of a subspace. (4) 3.2.21. Here, “explain” means that if the answer is yes always, prove it. If the answer is not necessarily, provide an explicit example proving that the statement may be false. (5) 3.2.14. Here, “explain” means that if the answer is yes always, prove it. If the answer is not necessarily, provide an explicit example proving that the statement may be false. 1...

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