# Find matrix of the linear function

1. Mar 5, 2012

### junsugal

1. The problem statement, all variables and given/known data

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)

2. Relevant equations

3. The attempt at a solution

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

Last edited: Mar 5, 2012
2. Mar 5, 2012

### tiny-tim

hi junsugal!

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

do it for each basis element separately

what do you get?

3. Mar 5, 2012

### junsugal

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! :)

4. Mar 5, 2012

### tiny-tim

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