(2) Let V be an inner product space. Let u and v be nonzero vectors in V such that for every w E V, one has (u, w) = 0 whenever (v, w) = cE F. 0. Prove that u = cv for some

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Q: 5) Let V, W be finite dimensional vector spaces over F. (a) ( Prove that (b) Use this to prove that…

A: Question is wrong • please see the justification

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A: Let 'V' be vector space over field 'F'  Standard basis  elements of ℝ3 are given as: (1,0,0),…

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Q: (10) Let the vector space P, has the inner product (p(x), q(x)) = | P(x)q(x)dx (a) Compute ||p(x)||…

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Q: Let V be a vector space over F. Let a E F and v E V satisfy the equation av = 0. Prove that either a…

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Q: Let V be a vector space, u a vector in V, and c a scalar. Prove 0u= 0

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Q: 32. In a normed vector space (V, ||) show that B,(x) = x + B,(0) = {x + y: Ilyll <r} and that B,(0)…

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Q: Use the inner product (f, 9) = | $(2)g(x) dæ f(r)g(r) dr in the vector space C°[0, 1] of continuous…

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Q: H, ond H2 are subuedɔr spoces of vector space, Sp (H, U Ha) - H, +H2 show that I

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Q: Let u and v be vectors in an inner product space V. If ((u − v), (u + v)) = 0, show that u=v.

A: Given, u and v be vectors in an inner product space V. ((u − v), (u + v)) = 0

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Q: Let V be a real vector space with inner product 〈,〉. Prove that for any u,v,w ∈V 〈u,v〉〈u,w〉≤…

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Q: Consider the real vector space M2x3(R) with the usual inner product (A, B) = tr (B' A) Given the…

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Q: Let V be a finite-dimensional inner product space over C and let u, w€ V be fixed non-zero vectors…

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Q: If S and T are two subsets of a vector space V (F) and S cL (T) then show that L(S) CL (T).

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Q: 6. Let V be an inner product vector space. (A) For any u, v E V , assume that (u, v) E R. Prove the…

A: Given that V be an inner product vector spaceA) u,v∈V, prove the identityu,v=14u+v2-14u-v2

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