Span of vectors

  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. mathwonk

    mathwonk 9,703
    Science Advisor
    Homework Helper

    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. lurflurf

    lurflurf 2,327
    Homework Helper

    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. Is it the x-z plane in R^3?
     
  6. mathwonk

    mathwonk 9,703
    Science Advisor
    Homework Helper

    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. The main diagonal line in x-z plane
     
  8. mathwonk

    mathwonk 9,703
    Science Advisor
    Homework Helper

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