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  3. consider n-dimensional finite affine space: f(n,p)

Consider n-dimensional finite affine space: F(n,p) over the field with prime p-elements. a. Show tha if l...

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Advance Math

Consider n-dimensional finite affine space: F(n,p) over thefield with prime p-elements.

a. Show tha if l and l' are two lines in F(n,p) containing theorigin 0, then either l intersection l' ={0} or l=l'

b. how many points lie on each line through the origin inF(n,p)?

c. derive a formula for L(n,p), the number of lines through theorigin in F(n,p)

Answer & Explanation Solved by verified expert
4.0 Ratings (442 Votes)
By definition the ndimensional finite affine space Fnp Fpn a1a2an aiFp i12n where Fp is the field withprime p elementsThis forms a vector space over Fp of dimension naNow any line through the origin 0 is the subset ka k Fp for some vector a Fnp 0This is a vector subspace of Fnp of dimension 1 namely    See Answer
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