Proof about bases for subspaces

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Homework Help Overview

The discussion centers around proving that all bases for a subspace V of R^N contain the same number of elements, which relates to concepts in linear algebra and vector spaces.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about how to begin the proof, with one suggesting the need to find an equation of the subspace. Another participant attempts to clarify the problem by assuming two bases and questioning how to show their sizes are equal.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and attempting to clarify their understanding of the concepts involved. Some have begun to outline their thoughts on the relationship between bases and the elements of the subspace.

Contextual Notes

There is a noted lack of clarity regarding the initial steps needed to approach the proof, and participants are questioning the definitions and properties of bases and linear independence.

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Homework Statement


Prove that all bases for subspace V of R[tex]\hat{}N[/tex] contain the same number of elements.


Homework Equations





The Attempt at a Solution



I have absolutely no idea where to start this proof. Do I need to do something with finding an equation of the subspace, or not?
 
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R^n

like, real numbers in all dimensions. I tried typing it using LaTeX and failed.
 
I think I got started

assuming I have 2 bases of V, (w1, w2, ...wn) [tex]\in[/tex]O R[tex]\hat{n}[/tex]

and (v1,v2,...vp)[tex]\in[/tex]O R[tex]\hat{n}[/tex], I'm supposed to be showing that n=p

But I'm not sure how to do that.
 
a basis is a linearly independent set that spans the space, thus any element of V can be written in terms of W and vice versa...
 

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