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# X3 these two equations are essentially dierent as in

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Unformatted text preview: ts, namely, X 1 + 2 X 2 + 3 X 3 − X 4 = 0, 2 X0 − X1 + 4 X2 − = 0. X3 These two equations are essentially diﬀerent, as in the two ratios formed by picking up the coeﬃcients of the two equations are distinct: 0 : 1 : 2 : 3 : −4 = 2 : −1 : 4 : −1 : 0 . So, the system X 1 + 2 X 2 + 3 X 3 − X 4 = 0, 2 X0 − X1 + 4 X2 − = 0. X3 indeed gives a 2-plane inside P4 (X0 X1 :X2 :X3 :X4 ) . Now, what is asked in (3) is to oﬀer the Pl¨cker coordinate of the 2-plane deﬁned by this last system. The answer: u : 0 2 1 −1 2 4 : 2 : 4 3 −1 : 13 −1 − 1 : 23 4 −1 01 2 −1 0 2 : 0 −1 20 : 1 −1 : −1 0 2 4 −1 0 : 3 −1 −1 0 = − 2 : −4 : −6 : 2 : 6 : 2 : −1 : −14 : 4 : −1 . 5 ⋆ The following is the fact cited in the solution above from “Review of Lectures – XXIX” . Assumption 1. Let k and n be positive integers, such that k ≤ n. Let π1 , π2 , · · · , πk be distinct k number of points in Pn . Assume that, for each j with 3 ≤ j ≤ k , no subset πi1...
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## This note was uploaded on 01/12/2014 for the course MATH 660 taught by Professor Yasuyukikachi during the Fall '13 term at Kansas.

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