Let P3 be the set of all polynomials of degree at most 3. That is P3 = {ao + ait + azt? + azt³ | ao,a1,a2, a3 E R}. With the zero polynomial po(t) = 0, the usual addition, and the usual scalar...

Extracted text: Let P3 be the set of all polynomials of degree at most 3. That is P3 = {ao + ait + azt? + azt³ | ao,a1,a2, a3 E R}. With the zero polynomial po(t) = 0, the usual addition, and the usual scalar multiplication, P3 is a vector space. Let H = {bo + bit + b3t | bo, b1, b3 E R} be a subset of P3. (a) Give a nonzero polynomial h1 (t) in H, and a polynomial h2(t) in P3 which is not in H. (b) Show that H is a subspace of P3. (c) Give a basis for H (you must show why is it a basis for H). What is the dim(H)?