Do the given vectors form an orthogonal basis for ℝ3? v1 = 1 0 −1 , v2 = 2 4 2 , v3 = 3 −3 3 Yes, the given set does form an orthogonal basis for ℝ3. No, the given set does not form an orthogonal basis for ℝ3. You are given the theorem below. Let {v1, v2, , vk} be an orthogonal basis for a subspace W of ℝn and let w be any vector in W. Then the unique scalars c1, , ck such that w = c1v1 + + ckvk are given by ci = w · vi vi · vi for i = 1, , k. Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w]basis B of w with respect to the basis basis B = {v1, v2, v3} of ℝ3. w = 1 1 1 [w]basis B =