this is the question.

4. (16 points) Recall that P2 is the vector space of polynomials with real coefficients and with degree less than or equal to 2 (equipped with the natural operations on polynomials). Consider the linear map L : P2 - P2 defined by its action on the canonical basis B= as follows: L(x?) = -4x +6x, L(x) =-4x+3 and L(1) =-4. Lastly, let p be the polynomial given by p = 2x+ 1-x2. (a) Find the matrix representation H = Repgg(L) of the map h with respect to the basis B. (b) Find the column vector representation, Repg(p) or [p]g, of the polynomial p with respect to the basis B. (c) Use the matrix obtained in part (a) and the result of part (b) to find the column vector [L(p)]B