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How many vectors in span({v}) 
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#1
Sep1609, 10:57 PM

P: 29

1. The problem statement, all variables and given/known data
Let v be an element of F^{2}_{p} \ {(0,0)}. How many vectors does Span({v}) have? How many 1dimensional vector subspaces does F^{2}_{p} have? F^{2}_{p} is the twodimensional field (a,b) where each a, b are elements of F_{p}, where p is a prime number. 3. 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. 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
Sep1609, 11:02 PM

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An element in span(v) must be of the form av for some a in the field. How many choices of a do you have? Do all of these choices yield a different vector, or can av=bv if a=/=b?



#3
Sep1609, 11:07 PM

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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?



#4
Sep1609, 11:17 PM

P: 29

How many vectors in span({v})



#5
Sep1609, 11:21 PM

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P: 25,247




#6
Sep1609, 11:22 PM

P: 29




#7
Sep1609, 11:59 PM

P: 29




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