3. Consider V = {a2x² +a1x + ao € P2(R) : a2 + a1 + ao = 0} . Use the subspace theorem to show that V is a subspace of P, (R).

Find the orthogonal complement of the subspace W span{v₁, v₂} where, = || -- , V2 0

Find the orthogonal projection of v=(−5,2,−10,6) to the subspace W of R4 spanned by (3,−6,−4,−1) and (−4,−5,7,−10).projW(v) Then find the component of v orthogonal to W

4. Prove that W = {(2s + 4t, 2s, 2s - 3t, 5t): s, t ≤ R} is a vector subspace of R4 by using the Subspace Test.