General Lin. Alg. Span Question

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Homework Help Overview

The discussion revolves around the concept of vector spans in linear algebra, specifically questioning whether a set of three vectors can span a four-dimensional space, R4.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the dimensionality of vector sets and their relationship to the dimensionality of the space they are attempting to span. There is a focus on the implications of having fewer vectors than the dimensions of the space.

Discussion Status

Some participants express confidence in the assertion that three vectors cannot span R4 due to dimensional constraints. However, the discussion reflects varying levels of certainty and invites further exploration of the underlying principles.

Contextual Notes

Participants are considering the definitions of spanning sets and bases in the context of linear algebra, with an emphasis on the dimensionality of the vectors involved.

hydralisks
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If a question asks "does v1, v2, v3 span R4"
can i just say no, regardless of what v1 v2 v3 is
because v1 v2 and v3 is just 3 dimensions while R4 needs 4 dimensions?
 
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hydralisks said:
If a question asks "does v1, v2, v3 span R4"
can i just say no, regardless of what v1 v2 v3 is
because v1 v2 and v3 is just 3 dimensions while R4 needs 4 dimensions?

I'm almost sure you're right on this.
 
Thanks!
 
Yes. If a set of vectors spans a space, then some subset of it forms a basis for the space. Since no subset of 3 vectors can span a four dimensional set, this set cannot span R4.
 

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