01:640:250 Lecture 1: Vector Algebra

3) (10 pt) Let P = {ao + al X + a2X2?A3X3 I ao, ai , a2,A3 E R. Define T : Ps ? Ps determined by T(P(X)) P'(X)-XP"(X) (where P'(X) and P"CX) are the first and second derivative of P(X)). Show that T is a linear map. Find a basis for ker(T). What is the dimension of Range(T)?

Find the equation of the parabola y = a + bx + cx^2 that passes through the points. (1, -2), (2, 3), (3, 12)

7. Compute arc length of CX-3t, y = 3 for 0s t