Consider the 2-dimensional R-vector space V = C. Define a bilinear form on C by: (x, y) := Re(ry), for , y E C. This is a function C x C -> IR. Here Re(2) refers to the real part of z, and z is the complex conjugate of z. Determine which of the following statements are true. (A) (No answer given) + (1 + i,5 -1) >0 (B) (No answer given) + (., .) is an inner product on C, but it is not symmetric. (C) (No answer given) + A bilinear form is called positive definite if there exists a non-zero vector x such that (x, x) > 0. (D) (No answer given) + An inner product is a bilinear form which is both symmetric and positive definite. Marking: For each correct answer: +25% Blank answer: 0% For each incorrect answer: -12.5% Let V = P2(R) := {do + at + a2x2 | a; ER}, and let (., .) be the bilinear form defined as (f,g) := f(t)g(t) at ; this defines an inner product on V. Determine which of the following statements are true. (A) (No answer given) + The constant function 1 has length 1 in this inner product space. (B) (No answer given) + For any f, g E P2 (IR). (f, f) + (9, g)