Then, similarly, verify Proposition 2.13, using the span of ((2,3,1),(1,-1,2)) for U, and using F^3 for V.
Recall that dim P_m(F) = m+1. Thus, Theorem 3.18 guarantees that P_m(F) is isomorphic to F^(m+1). Now pick nice bases of P_m(F) and F^(m+1), and describe the invertible linear map T that shows they are isomorphic.