Is this Set and Operation a Vector Space?

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Homework Help Overview

The discussion revolves around determining whether a given set and operation constitute a vector space, focusing on the relevant axioms that define vector spaces.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of vector spaces and the associated axioms, with some expressing confusion about how to apply these axioms to the specific problem at hand.

Discussion Status

There is an ongoing exploration of the vector space axioms, with some participants suggesting a step-by-step approach to verify if the set and operation meet the criteria. However, no consensus has been reached on the specific application of these axioms to the problem.

Contextual Notes

Some participants question the original poster's understanding of vector spaces and the axioms, indicating a potential gap in foundational knowledge that may affect the discussion.

heytheree
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question in attachment. please help!
 

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Well what do you need help with?
 
im confused on how to prove this
 
What are the vector space axioms? Once you have these listed, then check if your space satisfies each of these axioms.
 
whats a vector axiom?
 
Do you know what a vector space is?
 
Clearly whoever gave you this problem expects you to know what a "vector space" is. The various "rules" given in the definition of "vector space" are the "vector space axioms" jgens is referring to.
 
yeah..i know what a vector space is..
 
heytheree said:
yeah..i know what a vector space is..

Ok, then just go 1-by-1 through the axioms and see if this set and this operation "pass" each one. If it doesn't pass one, then it isn't a vector space.
 

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