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Subspaces; Linear span

  1. Jun 22, 2009 #1
    1. The problem statement, all variables and given/known data
    (i)Show that the linear span of the vector a1 = (-7, 8, 5) is the line whose equation is
    x/(-7) = y/8 = z/5

    3. The attempt at a solution
    The problem is, I don't know where or how to start.
     
  2. jcsd
  3. Jun 22, 2009 #2

    Dick

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    Define the 'linear span of a vector'. Look it up if you have to.
     
  4. Jun 22, 2009 #3
    The linear span of a vector is the collection of all linear combinations of the vectors a1, a2..., ak
     
  5. Jun 22, 2009 #4

    Dick

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    Ok, so for one vector v1 it's the set of all vectors k*v1 for k any real number, right?
     
  6. Jun 23, 2009 #5
    Ya, and then?
     
  7. Jun 23, 2009 #6

    Dick

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    You are supposed to be helping here. Guess. (x,y,z) is a point in the span of (-7, 8, 5). What's it equal to?
     
  8. Jun 23, 2009 #7
    Okay so
    -7k = x
    8k = y
    5k = z
     
  9. Jun 23, 2009 #8
    Got it, thank you so much. I'll be back with more for sure lol.
     
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