1 b2 b3 1

Apply the Gram-Schmidt orthonormalization process to transform the given basis for R" into an orthonormal basis. Use the vectors in the order in which they are given. B = {(15, 8), (0, 1)} u2 II

Let p (x) = ao + a1x + a2x² and q (x) = bo + b1x + bɔx² be vectors in P2 with inner product = aobo + a¡b1 + azb2 . %3D Consider the polynomials in the set {-1+ x², 2+ x + æ²} 1. Show that the polynomials in the set do not form an orthonormal set. 2. Use the Gram-Schmidt orthonormalization process to form an orthonormal set from these polynomials. Keep the order, and show work for the orthogonalization, then normalization. 3. Do the polynomials in the orthonormal set (from question 2) form a basis for P, ? Why or why not?

Practice Another X Use the inner product (u, v) = 2u1V₁ + U₂v₂ in R2 and the Gram-Schmidt orthonormalization process to transform {(-2, 1), (-2, 3)} into an orthonormal bas (Use the vectors in the order in which they are given.) U1 = 4₂ =

Find an orthonormal basis of the subspace spanned by the vectors in Exercise 3.