4) Use the Gram-Schmidt process to transform the given basis, B, into an orthonormal one, B'', using the Euclidean inner product (dot product). You don't need to simplify the B'' vectors. 8 points total.
1. Let B = {v1, ..., vn} be a basis for an inner product space V.
2. Let B' = {w1, ..., wn}, where wi is given by:
w1 = v1
w2 = v2 - (⟨v2, w1⟩ / ⟨w1, w1⟩) * w1
w3 = v3 - (⟨v3, w1⟩ / ⟨w1, w1⟩) * w1 - (⟨v3, w2⟩ / ⟨w2, w2⟩) * w2
Then B' is an orthogonal basis for V.
3. Let ui = wi / ||wi||.
Then B'' = {u1, ..., un} is an orthonormal basis for V.
B = {(2, 0, 2), (4, 2, 4), (2, 2, 4)}