Problem 4. Let Pn(R) denote the vector space of polynomials over R with degree less than or equal to n. (F R)-{a + br + cr2 + dr3 l a, b, c, d E R}). Define L from Ps(R) to ,(R) such that the value L(p) of L on the polynonial p ? P3(R) is defined by or example, P40 where p denotes the derivative of p. (a) (10 pts.) Show that L : P3(R) ? PAR) is a linear operator (or linear transformation) (b) (10 pts.) Find a basis for the null space (or kernel) of L (c) (10 pts.) Find a basis for the range of L