Suppose that V is finite dimensional real vector space and that ⟨⋅, ⋅⟩ is an inner product on V. Let f∶V → R be a linear transformation. Prove that there exist a unique vector v∈V such that f(u)=⟨u,v⟩ for every u∈V. Suppose V = P2(R). Find the unique polynomial q ∈ V such that p(1)= ∫(integral -1 to 1) p(t)q(t)dt for every p∈V

Suppose that V is finite dimensional real vector space and that ⟨⋅, ⋅⟩ is an inner product on V. Let f∶V → R be a linear transformation. Prove that there exist a unique vector v∈V such that f(u)=⟨u,v⟩ for every u∈V. Suppose V = P2(R). Find the unique polynomial q ∈ V such that p(1)= ∫(integral -1 to 1) p(t)q(t)dt for every p∈V

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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