Chapter 4.3, Problem 50E

In Exercises 48 through 53, let V be the space spanned by the two functions $\cos \left(t\right)$and $\sin \left(t\right)$. In each exercise, find the matrix of the given transformation T with respect to the basis $\cos \left(t\right),\sin \left(t\right)$, and determine whether T is an isomorphism.

50. $T\left(f\right)=f^{″}+a{f}^{\prime }+bf$ , where a and b are arbitrary real numbers. Find all the values of a and b such that T is an isomorphism.