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Homework 3 Solution

# Homework 3 Solution - Math 660 GEOMETRY I SOLUTION FOR...

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Math 660 GEOMETRY I SOLUTION FOR REGULAR HOMEWORK – III (10/03) October 10 (Thu), 2013 Instructor: Yasuyuki Kachi Line #: 26471. [I] (8pts) (1) True or false : The system (#) a 1 X + b 1 Y + c 1 Z + d 1 W = 0 , a 2 X + b 2 Y + c 2 Z + d 2 W = 0 defnes a line in P 3 ( X : Y : Z : W ) , provided at least one oF a 1 , b 1 , c 1 and d 1 is non-zero ; at least one oF a 2 , b 2 , c 2 and d 2 is non-zero, and moreover p a 1 : b 1 : c 1 : d 1 P n = p a 2 : b 2 : c 2 : d 2 P . ” The answer is true . See “Review of Lectures – IX”, page 8, DeFnition. (2) True or false : Suppose at least one oF a 1 , b 1 , c 1 and d 1 is non-zero ; at least one oF a 2 , b 2 , c 2 and d 2 is non-zero, and moreover p a 1 : b 1 : c 1 : d 1 P n = p a 2 : b 2 : c 2 : d 2 P . Then at least one oF v v v v a 1 b 1 a 2 b 2 v v v v , v v v v a 1 c 1 a 2 c 2 v v v v , v v v v a 1 d 1 a 2 d 2 v v v v , v v v v b 1 c 1 b 2 c 2 v v v v , v v v v b 1 d 1 b 2 d 2 v v v v , v v v v c 1 d 1 c 2 d 2 v v v v is non-zero. The answer is true . See “Review of Lectures – XI”, page 8, Observation 1.

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• Fall '13
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Homework 3 Solution - Math 660 GEOMETRY I SOLUTION FOR...

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