Question

2. We briefly mentioned the linear map of differentiation on P2, namely d (ax2+

   dx

   bx+c) = 2ax+b.

   1. (a) Does this map have any eigenvalues/eigenvectors? What are they and

      how do you know? (recall what is special about an eigenvalue of 0?).

   2. (b) Can you think of a function, not necessarily a polynomial, which is an

      eigenvector of differentiation with eigenvalue 1?

   3. (c) More generally, an eigenfunction with eigenvalue k for the differentiation

      map is a solution to the differential equation y′ = ky.

      What is the general solution to this differential equation?

Answer 1