Ok, I think I got it. It took me many pages on my notebook...
***and after that I must change it back to R_4[x]...
and below I simply transform from
Does there exist a linear transformation so that and
So I got to this...
And if I prove it for the bases, I prove it for the entire thing. But how do I continue from here?
I know in general that if you have a basis you can create any transformation you want but I don't know how to.
Oy! Sorry, I always do that. I try to save time so I just give half the question... Maybe later, if I have more time, I'll just post the entire question with my answer and hopefully itwill be right.
I edited it at the top of my original post. Both spaces are in R_4[x]. Sorry for the confusion