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If span(S)=span(P), then S=P.

  1. Oct 30, 2006 #1
    I have just had linear algebra exam, and one of the questions was to prove or disprove (give a counterexample) that if span(S) = span(P) then S=P.

    I gave this example:

    S={v} where vector v=(1,2), and P={u} where u= (2,4).
    Then, span(S) = span (P) (line through origin parallel to vector (1,2)),
    but S does not equal P.

    Am I right?
    Thank you!
     
  2. jcsd
  3. Oct 30, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, that's perfectly correct. (And it was kind of a silly question!)
     
  4. Oct 30, 2006 #3
    Thank you! I spent 15 minutes proving that, and then decided to find a counterexample. I was confused because it seemed so easy once I got the idea. Thanks again!
     
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