Hello

right now Im studying for my linear algebra exam and I think I pretty much understood the basic concepts but then I tried the following and I am not able to solve it, can someone help me with this:

In the vector space

is U a subspace with the following polynomials as basis

:

Additionally there are the following functions:

which form a family

a) Calculate the Transformation Matrix

and the inverse.

b) Show why

is a basis

c) Calculate the Coordinates

of

d) For the linear map

calculate the Transformation matrices

and

.

I have no clue how to begin. I think i know how to solve b) and inverting a matrix is not a problem but the rest is not clear to me!

Can you help me, please!