1) The linear transformation L defined by L(p(x)) = p'(x) + p (0) maps P3 into P2. (a) Find the matrix representation of L with respect to the ordered bases {1,x,x2} and {1, 1-x}. (b) For the vector,...

Extracted text: 1) The linear transformation L defined by L(p(x)) = p'(x) + p (0) maps P3 into P2. (a) Find the matrix representation of L with respect to the ordered bases {1,x,x2} and {1, 1-x}. (b) For the vector, p(x) = 2x +x - 2 (i) find the coordinates of L(p(x)) with respect to the ordered basis {1, 1-x}, using the matrix you found in (a). Remember to use the coordinate vector of p(x) with respect to the basis {1, x, x2}. (ii) Show that they are the weights that work by writing the linear combination with the basis elements and comparing the resulting polynomial to L(p(x)).