Question4 and question5 plz

4. Let T be defined as a transformation, T : P1 - P2, such that T(p(x)) = fp(t)dt. That is, T is the operation of taking the definite integral over the interval [0, x]. Note, the end point of the interval is r, thus the result of the definite integral is still a polynomial. (a) What is T(2x + 1)? (b) Determine a basis for ker(7). What is the dimension of ker(T)? (c) Find range(7) and determine a basis for range(7). What is the dimension of range(T)? (d) Find the inverse transformation for 7, or explain why the inverse transformation for T does not exist. 5. For each transformation T defined below, determine whether or not T is invertible, and if it is invertible, find T-1. (a) T: R' - R' is defined by T(x, y) = (-4x + 3y, -5x + 4y). (b) T : ' - R' is defined by T(x, y) = (x, 2x). (c) T : R3- R3 is defined by T(x, y, z) = (-2, -I, -y)