In Exercise 1 - 4, p(x) = 3 - 2x and q(x) = 1 + x + x2.
1. (p(x), q(x)) is the inner product of example 7.4. Compute
(a) (p(X), q(x))
(b) ||p(x)||
(c) d(p(x), q(x))
2. (p(x), q(x)) is the inner product of Example 7.5 on the vector P2 [0, 1]. Compute
(a) (p(x), q(x))
(b) ||p(x)||
(c) d(p(x), q(x))
3. In Exercise 5, find a nonzero vector orthogonal to p(x).
4. In Exercise 6, find a nonzero vector orthogonal to p(x).