P22.3. Equipe the coordinate space R' with the weighted (or non-standard) inner product defined, for all vectors u := ul u2 u3 u4 us and v := [v1 V2 v3 V4 VS] , by (u, v) : (ulVI + 15u2v2 + 20u3v3 + 12u4v4 + 12usv5) . (i) Verify that the three vectors w1 : 8 -4 -1 -7 -7 , w2: 6 -2 0 1+ 15 1-V5]T, and w3 : 5 1 -1 0 0] are pairwise orthogonal. (ii) Calculate the norms of the vectors w1, w2, and w3. (iii) Compute the orthogonal projection of the vector z := 11 3 -4 -9 -9 onto the linear subspace W := Span(w1, W2, W3)