Let V be the ℝ-vector space of real-valued continuous functions on the interval [0, π] with the inner product given by ⟨f, g⟩ = ∫0π f(x)g(x)dx. Let S = {sin(x), cos(x), sin2(x), cos2(x)} and W be the subspace of V generated by S. Which of the following statements is true?

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Mathematics · Linear Algebra

Verified Solution4 OptionsUpdated: October 2026👁️1 View

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Correct answer

There exist f, g ∈ S such that ⟨f, g⟩ = 0.

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Answer 1

S contains an orthonormal basis of W.

Answer 2

There exist f, g ∈ S such that ⟨f, g⟩ = 0.

Answer 3

S is an orthonormal basis of W.

Answer 4

S is a basis of W.

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