9. Consider the orthonormal basis S for R³ S = (v₁,v₂,v,} where v₁ = (0,1,0) and v₁ = Let u = V₂ = = (1,0,4). Find (u), 8 A (u), = (0,-3, 135) B (M), - (1,3,7) = C (u), - (0, 3, 1/2) = D No correct answer E (u) = (0,8,19)

The vectors p1(t) = 1 + t², p2(t) = −t + 3t², and p3(t) = 1+t+t2 form a basis B 2(t), p3(t)} for P₂(R). Let p(t) = 1 + 2t + 4t², find its B-coordinates [p(t)B. =

Apply Gram-Schmidt to (1, 0, −1, 1), (2, 1, −1, 0) , (2, −1, −1, 3) to obtain an orthonormal set with the same span as these vectors.

2 [H] a) Treating u, v', and w' as vectors, are the following inner products defined? (i) u. v' 6) (True/False) Let u = (ii) v'. u (iii) u - w' v' = [1 3 2], and w' = [5 -1 -1]. b) Treating u, v', and w' as matrices, are the following matrix products defined? (i) uv' (ii) v'u (iii) uw'