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Let 71, 72, 73, 74, 75, 76 be six planes in three-dimensional projective space such that each of the following sets of three planes have a common line of intersection {T1, T2, T3}, {1, T4, T5}, {3, 75, 76}, {72, 74, 76}. Further, no four planes have a common line of intersection. Prove that the six planes have a common point. (Hint: Solve the dual problem.)

Let 71, 72, 73, 74, 75, 76 be six planes in three-dimensional projective space such that each of the following sets of three planes have a common line of intersection {T1, T2, T3}, {1, T4, T5}, {3, 75, 76}, {72, 74, 76}. Further, no four planes have a common line of intersection. Prove that the six planes have a common point. (Hint: Solve the dual problem.)

Advanced Engineering Mathematics
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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Let 71, 72, 73, 74, 75, 76 be six planes in three-dimensional projective space such that each of the following sets of three planes have a common line of intersection {71, 72, 73}, {1, T4, T5}, {3, 75, 76}, {72, 74, 76}. Further, no four planes have a common line of intersection. Prove that the six planes have a common point. (Hint: Solve the dual problem.)
Transcribed Image Text:Let 71, 72, 73, 74, 75, 76 be six planes in three-dimensional projective space such that each of the following sets of three planes have a common line of intersection {71, 72, 73}, {1, T4, T5}, {3, 75, 76}, {72, 74, 76}. Further, no four planes have a common line of intersection. Prove that the six planes have a common point. (Hint: Solve the dual problem.)
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