Two quick linear algebra problems
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Two quick linear algebra problems

[From: ] [author: ] [Date: 12-01-09] [Hit: ]
Show why the set of all ordered pairs of real numbers (x, y) with addition defined as u + v = (u1 + 2v1, u2 + 2v2) and scalar multiplication as ku = (ku1, ku2) is not a vector space-1.........
1. It is known based on a theorem that any set of 7 vectors in R6 will be linearly independent, does this guarantee any set of 5 vectors in R6 will be linearly independent? why?

2. Show why the set of all ordered pairs of real numbers (x, y) with addition defined as u + v = (u1 + 2v1, u2 + 2v2) and scalar multiplication as ku = (ku1, ku2) is not a vector space

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1...your "theorem " knowledge is false...7 in R6 is LD not LI

and a , b , a +b , c , a+b + c are 5 vectors in R6 which are not LI

#2 . ( a + b ) + c ╪ a + ( b + c )
1
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