In each of the following exercises, we shall use the notation f(x) to denote the function x→f(x), x ε R. In each case, V will denote the vector space of all real-valued functions on the real line, with the vector operations defined point-wise. In each case, determine whether or not the given set is linearly independent and compute the dimension of the linear subspace spanned by the set.
18. {1, eax, ebx}, a≠b.
23. {1, cos2x, sin2x}.