This is a part of an exercise I got on the final exam I failed. I couldn't answer well this question : Let and the space of polynomials of degree .
a)Show that is isomorph to . (Done)
b)Does there exist 2 distinct isomorphisms? If so, give them. (Done. The answer was yes if it might help for the next question)
c)Tell whether there exist a linear transformation such that , , and .
My attempt :It doesn't exist because the vectors , , and are linear independent. And so , , and should... I stopped right there. I'm not sure of how to answer the question.