Question

HELP....Define D:P3->P3 such tat D(p(x))=p''(x). Let B={1,x,x^2,x^3}be a basis for P3. Find a matrix for the linear operator D with respect to the basis B.

Answer 1

Let's explore a little...

(d/dx) 1 = 0
(d/dx) x = 1 ----- (d/dx) 1 = 0
(d/dx) x^2 = 2x ----- (d/dx) 2x = 2
(d/dx) x^3 = 3x^2 ----- (d/dx) 3x^2 = 6x