Can a Set of 5 Vectors Span All of R6?

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Homework Help Overview

The discussion revolves around whether a set of 5 vectors in R6 can span the entire space of R6. Participants are exploring concepts related to vector spaces and their dimensions.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reason that 5 vectors might span R6 based on a memory of a teacher's advice, while others question the validity of this reasoning. Some participants express uncertainty about the dimensionality of vector spaces and how it relates to spanning sets.

Discussion Status

The discussion is ongoing, with participants questioning assumptions and definitions related to vector dimensions. Some guidance has been offered regarding the basic definitions of spanning sets and dimensions, but no consensus has been reached.

Contextual Notes

Participants are grappling with the implications of dimensionality in vector spaces, particularly in relation to the number of vectors needed to span R6. There is a noted lack of clarity regarding the fundamental definitions involved.

ykaire
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1. Can a set of 5 vectors in R6 span all of R6?I want to say that it does span, because i remember my teacher saying "don't think of the physical world," but I'm not entirely sure if it does.
 
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Neither of those are very good reasons for answering one way or another. Why do you think 5 vectors can span R^6?
 
Dick said:
Neither of those are very good reasons for answering one way or another. Why do you think 5 vectors can span R^6?


I'm not sure, to be honest.
 
How many vectors span R2? R3?
 
venom192 said:
How many vectors span R2? R3?
Um, I'm guessing that vectors span R2 and 3 Vectors span R3.
so... that must mean that 6 vectors span R6.
 
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Why are you doing all of this guessing? It looks to me like you need to review the basic definitions. You should know immediately that R6 has dimension 6. What does that mean. What can you say about any spanning set in a space of dimension n? What can you say about any linearly independent set in a space of dimension n?
 

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