Let S = {p1, p2, p3, p4} be a set of polynomials in the polynomial space P3, where p1(t) = 1 + t 3 , p2(t) = ?t + 3t 2 ? t 3 , p3(t) = 3 + t ? 2t 2 , p4(t) = 1 + t 2 ? 3t 3 . 1 (a) Determine whether S is a basis for P3. (b) Find a basis for the subspace W = span S AND determine the dimension of W. (c) Determine whether p(t) = ?4t + 12t 2 ? 4t 3 is in W = span S

3. (30 points) Let S = {p1, p2, p3, pa} be a set of polynomials in the polynomial space P3, where pi(t) = 1+ +, pz(t) = -t+ 3+2 - +, pa(t) = 3+t - 212, pa(t) = 1+ +2 -3+3. (a) Determine whether S is a basis for P3. (b) Find a basis for the subspace W = span S AND determine the dimension of W. (c) Determine whether p(t) = -4t + 1212 - 4+3 is in W = span S