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Vector Space

  • Thread starter hkus10
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  • #1
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1) How to show that if W is a subspace of a finite-dimensional vector space V, then W is finite-dimensional and dim W<= dimV.

2) How to show that if a subspace of a finite-dimensional vector space V and dim W = dimV, then W = V.

3) How to prove that the subspace of R^3 are{0}, R^3 itself, and any line or plane passing through the origin.

How to approach these three Questions?

Thanks
 

Answers and Replies

  • #2
HallsofIvy
Science Advisor
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You approach any "proof" by looking at the definitions! What is the definition of "finite dimensional" vector space? What is the definition of "dimension" for such a space?
 

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