Let V be the space C[0, 2] with the inner product of Example 7. Use the Gram-Schmidt process to create an orthogonal basis for the

Let V be the space C[0, 2π] with the inner product of Example 7. Use the Gram-Schmidt process to create an orthogonal basis for the subspace spanned by {1, cost, cos²t, cos³t}. Use a matrix program or computational program to compute the appropriate definite integrals.

EXAMPLE 7 For f, g in C[a, b], set (f. g) = f* f (1)g(1) dt a Show that (5) defines an inner product on C[a, b]. (5)