Apply the Gram-Schmidt process to obtain an orthonormal basis for the 51 space spanned by the vectors 4 6 Show your work.

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

The set of vectors {(1, 1, 0), (1, 0, 1), (0, 0, 1)} is an orthonormal basis for the space R^3 in some scalar product <.,.>. Then, the scalar product <(1, 1, 1), (1, 0, 0)> is equal to: (a) -1. (b) 0. (c) 1. (d) 2. (e) 4. The correct answer is (a). Why?

Find a basis for Q(3^(1/3), 3^(1/2)) over Q.