Find matrix of the linear function

[junsugal]

Homework Statement

Consider the linear function F : P₄ -> R⁵
that sends the basis {1,x,x²,x³,x⁴} of P₄ to the basis {e₁,e₁,e₃,e₄,e₅} in R⁵, in that order , that is F(xⁿ)= e_(n+1)).
(a) Is this function an isomorphism?
(b) Consider the linear function D : P₄-> P₄
p(x)->p'(x)

Find the matrix of the linear function T : R⁵-> R⁵ such that
(T o F)p(x) = (F o D)p(x)

Homework Equations

The Attempt at a Solution

I solved for part a, but i have no idea how to start on part b

 

[tiny-tim]

hi junsugal!

(try using the X² button just above the Reply box )

do it for each basis element separately

start with x⁴ …

what do you get? ​

 

[junsugal]

hmm, what do you mean by start with x⁴?

For part(a) I said that yes the function is isomorphic because P₄ and R⁵ both have dimension of 5. And according to one of the properties of isomorphic, the dimensions of 2 vector spaces should be the same.

Thanks for the tips! :)

 

[tiny-tim]

hmm, what do you mean by start with x⁴?

put x = x⁴ in (T o F)p(x) = (F o D)p(x)

(and your (a) is ok)