- #1
brru25
- 29
- 0
Homework Statement
Let v be an element of F2p \ {(0,0)}. How many vectors does Span({v}) have? How many 1-dimensional vector subspaces does F2p have?
F2p is the two-dimensional field (a,b) where each a, b are elements of Fp, where p is a prime number.
The Attempt at a Solution
I know the total number of elements in the vector space F2p \ {(0,0)} is p2 - 1. I also thought that this was the number of vectors in Span({v}) but I've told by a couple people that is not so. I started with the definition of span but I just couldn't see the rest unfold.
Thank you ahead of time for your help.