Let p (t), q (t) = (p (0) - p (1)) (q (0) - q (1)) + p (1) q (1). Determine if this is an interior

product on P2, ie the space of quadratic polynomials.

(b) Let F be defined by

F (p) (t) = (t + 1) p (t) + 2p (t) + tp (1).

Show that F is a linear image F: P2 P2. (2p)

(c) Describe the matrix for the mapping from (b) the information expressed in the base {1, t, t ^ 2}.