Let P₂ = {ao+ a₁t+ a₂t² | ªº‚ª₁‚ª₂€R} That is, P₂ is a linear space of all polynomials of degree two or less with standard basis u = {1, t, t²}. Let W = {f(t) € P₂ | f'(0)=0}. You may assume that W is a subspace of P2. a. Let g(t) = t² and h(t) = t. Show that g(t) € W and h(t) w b. Show that the set B = {1, t²} spans W by proving that if a polynomial f(t) = a + a₁t+ a₂t² is in W then a₁ = 0.
