3. Given the following V sets and scalar sets S, is V a vector space? Provide a detailed proof in each case. a) V = set of real-valued functions that have 2nd derivative in the [0, 1] interval; S = real numbers. b) V = 3X3 upper-triangular matrices with real entries; S = real numbers. 0) V: 2X2 symmetric matrices; S = complex numbers. 3.1 Pick one of the previous examples that corresponds to a vector space (whichever you want) and find a basis for that space