Problem 1 Let V be a vector space. Prove the following: • Let WCV, span (W) = W iff W is a subspace of V Let V1, V2, V3 EV be vectors. Show span (span (v1, v2), V3) = span(V1, V2, V3) ● Let V1, ..., Vk Є V where k ≥ 2. Suppose span (v₁, ..., Uk) of vector {1,..., Uk} is linearly dependant = span (v2,..., Uk). Show that the set Determine whether each set {P1, P2} is a linearly independent set in P3. Type "yes" or "no" for each answer. The polynomials p₁(t) = 1 + t² and p2(t) = 1 − t². The polynomials p₁(t) = 2t + t² and p2(t) = 1 + t. The polynomials p1(t) = 2t - 4t² and p2(t) = 6t² - 3t. (1~) i