Let P2 denote the vector space of all polynomials in the variable x of degree less than or equal to 2. Let B = {1, x, x^2} be an ordered basis for P2.
Write -2 + 7x + 4x^2 as a linear combination of elements from the basis B.
-2 + 7x + 4x^2
= 3x^2 + (-1 + 2x + 2x^2).
b. Let [q]B denote the coordinate representation of q relative to the basis B. Find the coordinate vector representation for -2 + 7x + 4x^2 relative to the basis B. Your answer should be a vector of the general form <1, 2, 3>.
[-2 + 7x + 4x^2]B