Please write this with all steps for a direct proof

2. Suppose {u1, u2, . .., u, } is an orthogonal set in a vector space ) with an inner product (., .). Find an orthonormal set {w1, w2, . ..,Wn} such that span { u1, u2, . . ., u} } = span {w1, w2, . . .; w} } for j = 1, 2, . . ., n