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Dimension of the linear span of a vector

  1. Jun 27, 2011 #1
    1. The problem statement, all variables and given/known data
    find the dimension of the linear span of the given vectors
    v1 = ( 2, -3, 1) v2 = ( 5, -8, 3) v3 = (-5, 9, -4)


    2. Relevant equations



    3. The attempt at a solution
    so all i did was make it a matrix and put it in rref and i got
    [1 0 0]
    [0 1 0]
    [0 0 1]

    does this mean dimensions of the linear span = 3?
     
  2. jcsd
  3. Jun 27, 2011 #2

    HallsofIvy

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    Science Advisor

    Yes, it does. What you have shown is that those three vectors are independent and independent vectors form a basis for their span.
     
  4. Jun 27, 2011 #3

    Dick

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    It would mean that. Except I think you did the row reduction wrong. Those vectors aren't linearly independent.
     
  5. Jun 27, 2011 #4
    oops i did i did it again and got

    1 0 5
    0 1 -3
    0 0 0

    so dimension = 2?
     
  6. Jun 27, 2011 #5

    Dick

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    Yes, dimension=2.
     
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