Prove PGL(V) Acts 2-Transitively on P(V) Projective Space

gankutsuou7
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Dim(V)>1.Prove that PGL(V) acts two transitively but not 3 transitively on P(V) projective space.
 
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Idea: Any two non-colinear vectors form a basis. Three vectors form a basis only when they are linearrly independent. You can't map linearly independent vectors to linearly dependent vectors by a GL(V) transformation.
 

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