- #1

johnson123

- 17

- 0

## Homework Statement

Show that F[x]/( g(x) ) is a n-dimensional vector space. where g is in F[x],

and g has degree n.

Its clear that F[x]/( g(x) ) is a vector space and that

B= (1,[tex]x^{2}[/tex],...,[tex]x^{n-1}[/tex]) spans F[x]/( g(x) ),

but I am having trouble showing that B is linearly independent

I realize this is pretty much a HW problem and it should be in the HW section, but I

read a post from one of the pf mentors noting that for gradlevel/seniorlevel problems

you might have a chance at a response from the non homework sections. thanks for any suggestions.