Consider the real vector space V = ℝ[x| equipped with an inner product. Let W be the subspace of V consisting of polynomials of degree at most 2. Let W⊥ denote the orthogonal complement of W in V. Which of the following statements are true?
1
There exists a polynomial p(x) ∈ W such that x4 - p(x) ∈ w⊥
2
W⊥ = {0}
3
W and W⊥ have the same dimension over ℝ
4
W⊥ is an infinite dimensional vector space over ℝ