Question 2 Check if each of the examples below represents a linear space (subspace), considering usual operations of addition and multiplication by scalar, unless instructed otherwise. For each of the linear spaces (subspaces) determine its dimension; for each case which is not a linear space (subspace), explain why it is not. (a) The set of all polynomials with a degree smaller or equal to 8 (b) The set of all functions f(x) = _ ak cos(k-1) (x) where ak E R and x E [0, T] K = 1 a + 2b (c) The set of all vectors of the form 3b + 4c (where a, b, c ER) 5c + 6 (d) The set of all symmetric 4 x 4 matrices of real numbers