Question: In Exercises, determine if the given set S is a subspace of the space C[0, 1] of all real valued functions that are continuous on the interval 0 ≤ x ≤ 1. Give reasons why either S is a subspace, or it is not.
Exercise: 1. S is the set of all polynomials of degree two.
2. S is the set of all polynomial functions.
3. S is the set of all continuous functions such that f(0) = f(1) = 0.