Mathematics · Linear Algebra
Consider the real vector space V = ℝ[x] of all polynomials equipped with an inner product. Let W be the subspace of V consisting of polynomials of degree at most 2. If W⊥ denotes the orthogonal complement of W in V, which of the following statements is true?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1W⊥ is an infinite-dimensional vector space over ℝ✓
- 2W and W⊥ have the same dimension over ℝ
- 3W⊥ = {0}
- 4W⊥ is a finite-dimensional vector space with dimension equal to 3
Correct answer
W⊥ is an infinite-dimensional vector space over ℝ
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