General Lin. Alg. Span Question

  • Thread starter hydralisks
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  • #1
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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?
 

Answers and Replies

  • #2
fluidistic
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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?

I'm almost sure you're right on this.
 
  • #3
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Thanks!
 
  • #4
HallsofIvy
Science Advisor
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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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