Quote by Dick
Take an example. Let F=Z_3, the field with three elements {0,1,2}. Yes, there are 8 elements in (Z_3)^2{0,0}. How many elements are in span((1,1))? That's (1,1)*x for all x in Z_3. Does that help you to see things unfold?

Would (1,1)*x have 3 elements? (1,1,0), (1,1,1), (1,1,2)? Or am I reading this incorrectly?