Elem lin algebra (Vector space question)

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Homework Help Overview

The discussion revolves around the properties of vector spaces in linear algebra, specifically questioning the existence of a zero vector within a defined vector space.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of a zero vector and its role as the additive identity in a vector space. There is a focus on whether a specific vector can serve as the zero vector despite not being in the conventional form.

Discussion Status

Some participants have offered insights into the nature of the additive identity, while others are questioning the specific form of the vector that could fulfill this role. Multiple interpretations of the vector space's properties are being explored.

Contextual Notes

There is an ongoing discussion about the implications of having a vector that does not conform to the standard zero vector representation and what that means for the vector space in question.

Miike012
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How is the following a vector space if it does not have a zero vector?
 

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If the space has a vector e such that x + e = x, for any vector x in the space, then e is acting as the zero vector. More formally, e is the additive identity.
 
but e = (0,0) is not of the form (1,x)
 
Miike012 said:
but e = (0,0) is not of the form (1,x)

But for this vector space, e ≠ (0, 0).

What is e for this vector space?
 
is it (1,0)?
 
Miike012 said:
is it (1,0)?
Yes, that's e .
 

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