The following vectors form a basis for R. Use these vectors in the Gram-Schmidt process to construct an orthonormal basis for R³. (Enter your answers as comma-separated lists. Enter each vector in the form (x,, X2, ..).) (а) (1, 1, 1), (2, 0, 1), (4, 8, 9) (b) (3, 2, 0), (1, 5, -1), (5, -1, 2)

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.

a) Find , \pl, d (p, q), and then find the angle between them for the polynomials in P2 if p(x) = -3x² + 2x – 5 , and q(x) = -x+5x? b) Verify that the basis set S = {(3,0,4), (-4,0,3), (0,1,0)} is orthogonal then find the coordinates of the vector u = (-5,5,1) using inner product