5. Let V be a vector space over a field F, and let U be a subspace of V. Using the fact that U is a subspace of V, prove that U is a vector space over F. (That is, verify closure under + and scalar multiplication and verify that (VS1)-(VS8) hold for U by using the fact that U is a subspace of V.)

Q: Let W be a subspace of a vector space V. Show that if x is in both W and W+, then x = 0.

A: Solution is given below

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A: According to the given information,

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A: B=sint, cost is a basis of H

Q: 2. Prove that every element in a vector space has a unique additive inverse.

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Q: 5. Prove that (-1)v=-v for every vector v in a vector space.

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A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

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Q: Let V be the vector space of polynomials in t of degree ≤ 3. Determine whether the following vectors…

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Q: Do 4

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