Commute Isomorphism & Friends problems

[MimpiBuruk]

Homework Statement

F:P₂->R⁵
F(x_n) = e_n+1
Consider the linear function
D:P₄ -> P₄
p(x) -> p'(x)
Find the matrix of the linear function T:R⁵ -> R₅ such that

Homework Equations

( T ° F ) p(x) = ( F ° D ) ( p(x) )

The Attempt at a Solution

T ° F ° F^-1 = F ° D ° F^-1
T = F ° D ° F^-1
then what should I do? thx

 

[vela]

You seem to have several typos in your post. Could you fix those please?

How do you know F is invertible?