
#1
Feb2508, 06:26 PM

P: 47

1. The problem statement, all variables and given/known data
Let R denote the set of real numbers. Define scalar multiplication by [tex]\alpha x = \alpha x[/tex] which is simply regular scalar multiplication, and vector addition is defined as [tex]x \oplus y = max(x,y)[/tex]. Is R a vector space with these operations? 2. Relevant equations Some given above. 3. The attempt at a solution There seems to be no zero vector to this equation as for any number k there exists another number k1, so there is no single 0 vector for a vector space with the operations defined above. Is this reasoning correct? 



#2
Feb2508, 08:53 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,904

Yes, that's true. So what is your answer to the question?




#3
Feb2708, 07:16 PM

P: 47

Then it is not a proper vector space!
Thanks a lot. 


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