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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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