Suppose that $V=V_{2}(q)$ is a vector space on a finite field $GF(q)$, so $|V|=q^{2}$. I saw this problem somewhere, " Describe one dimension subspaces of $V$ and find the number of them".
What I have done for this problem:
"I know that if we take such subspace, it would be like $
For the rest of above problem any help or hint will be appreciated. Thanks.