8 Let A be a finite afine plane so that, according to Major Exercise 2, all lines in A have the same number of points lying on them; call this number n. Prove the following: (a) Each point in A has n+ 1 lines passing through it. (b) The total number of points in A is n². (e) The total number of lines in A is n(n+ 1). (Hint: Use Major Exercise 7.)

8 Let A be a finite afine plane so that, according to Major Exercise 2, all lines in A have the same number of points lying on them; call this number n. Prove the following: (a) Each point in A has n+ 1 lines passing through it. (b) The total number of points in A is n². (e) The total number of lines in A is n(n+ 1). (Hint: Use Major Exercise 7.)

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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