Problem Set 16 In an earlier problem set, it was shown that any three points in A2 Summary: Problem Set 16 In an earlier problem set, it was shown that any three points in A2 can be moved to any other set by an ane change of coordinates. The next problem is a similar problem in Pn . Let V Pn be a set of points. V is said to be in linearly general position if any subset of V of size n + 1 does not lie on a hyperplane and if any subset of V of size k n does not lie on a k - 1-plane. Problem 1. Prove that any 2 ordered sets of n + 2 points in linearly general position in Pn are projectively equivalent. Problem 2. Can you nd a condition that allows you to determine when 4 points in P1 are projectively equivalent? Hint: Let the two sets be {P1, P2, P3, P4} and {Q1, Q2, Q3, Q4}. Move P1 to 1, move P2 to , and move P3 to 0. Where does P4 get moved? A modication of this procedure can be used to determine when n+3 ordered points in Pn are linearly equivalent (see pages 7,8,12 of Harris). An explicit answer Collections: Mathematics