3. Let p, (t) =1-3t+ 212 -4t', p,(1)=2-1+4t', p,(t)=-4-312 +7t' and pa(1)=-1-4t+3t' +3t' be polynomials in P. Also, let H = Span P, , P2 . P3,P.). a. Is the set ( P, , P2, P3, PAY linearly independent? b. Find a basis B for H. c. Does the set { P,, P2; P3, Pa) span P, ? d. Let p(t) =-5t-8t'. Is p in H? Explain. If so, write the coordinates of p with respect to the basis B you found in part a