Let v₁ = (1, 2, 0, 3, -1), v2= (2, 4, 3, 0, 7), v3 = (1, 2, 2, 0, 9), v4 = (-2,-4, -2, -2, -3). Find a basis of the Euclidean space R5 which includes the vectors V1, V2, V3, V4. estion 3 [2+3+3 marks]: a) Let {x,y} be linearly independent set of vectors in vector space V. Determine whether the set {2x, x + y} is linearly independent or not? W b) Suppose G is a subspace of the Euclidean space R¹5 of dimension 3, S = {u, v, w} [1 1 2 and Q are two bases of the space G and Ps = 1 2-1 be the transition matrix 1 from the basis S to the basis Q. Find [g]o where g = 3v-5u+7w. c) Let P₂ be the vector space of polynomials of degree ≤ 2 with the inner product: < p,q>= a₁ +2bb₁+cc₁ for all p = a +bx+cx², q = a₁ + b₁x + ₁x² € P₂. Find cos 0, where is the angle between the polynomials 1 + x+x² and 1-x+2x².