Problem 6.2.
a) In R3 with a standard scalar product, apply the Gram-Schmidt orthogonalization to vectors {(1, 1, 0), (1, 0, 1), (0, 1, 1)}.
b) Consider the vector space of continuous functions ƒ : [-1; 1] → R with a scalar product (f,g) := f(x)g(x)dx. Apply the Gram-Schmidt orthogonalization to {1, x, x2, x3}.