A) Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to 2. Let C={3,1+x, 3−3x+3x^2} be an ordered basis for P2.

b) Write −3+12x−9x^2 as a linear combination of elements from the basis C: −3+12x−9x2= (3)(c1)+ (1+x)(c2) +(3−3x+3x2)(c3).

c) Let [q]C denote the coordinate representation of qq relative to the basis C. Find the coordinate vector representation for −3+12x−9x^2 relative to the basis C. Your answer should be a vector of the general form <1,2,3>.