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Homework Help: Basis math help

  1. May 6, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine whether the set is a basis for R3.

    [3, -8, 1] , [6, 2, -5]

    3. The attempt at a solution

    I know it does not span R3, but the book says it is a basis for a plane in R3. How is it a plane?
  2. jcsd
  3. May 6, 2008 #2
    It doesn't span R3, but it does span R2, which you can think of as a plane in R3.
  4. May 6, 2008 #3


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    Homework Helper

    You first have to prove that the 2 vectors are linearly independent. To do that, recall the definition of linear dependence for 2 vectors. What does it mean for 2 vectors to be linearly dependent? If it doesn't satisfy that definition, and if none of the vectors is the zero vector, then you would have 2 linearly independent vectors.

    If you have only 1 linearly independent vector, then the linear span of that vector would be a line.

    The linear span of 2 linearly independent vectors is a plane in R^n.
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