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Span of vectors

  1. Jun 30, 2005 #1
    I'm stuck on the following problem:

    Describe the span of the vectors u1 and u2 in R^3, where
    u1 = (1, 1, 1), u2 = (1, −1, 1)

    I know that the span is a(u1)+b(u2), which becomes (a+b,a-b,a+b), but I don't know where to go from here.

    TIA.
     
  2. jcsd
  3. Jun 30, 2005 #2

    mathwonk

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    do you know gaussian elimination, reduction for matrices?

    i.e. how to solve for all vectors perpendicular to both of those?

    or you could just look at your general vector, since it satisfies an obvious equation.
     
  4. Jun 30, 2005 #3

    lurflurf

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    Consider (1/2)(u1-u2)=(0,1,0) and (1/2)(u1+u2)=(1,0,1)
    It will then be easier to see what is happening.
     
  5. Jun 30, 2005 #4
    Is it the x-z plane in R^3?
     
  6. Jun 30, 2005 #5

    mathwonk

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    have you noticed that the first and third entries of your vectors are equal? what does that tell you about an equations characterizing these vectors?
     
  7. Jun 30, 2005 #6
    The main diagonal line in x-z plane
     
  8. Jun 30, 2005 #7

    mathwonk

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    i.e. x=z describes all of these vectors.
     
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