- #1

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## Homework Statement

Let

*v*be an element of F

^{2}

_{p}\ {(0,0)}. How many vectors does Span({v}) have? How many 1-dimensional vector subspaces does F

^{2}

_{p}have?

F

^{2}

_{p}is the two-dimensional field (a,b) where each a, b are elements of F

_{p}, where p is a prime number.

## The Attempt at a Solution

I know the total number of elements in the vector space F

^{2}

_{p}\ {(0,0)} is p

^{2}- 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.