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Linear (in)dependence

  1. Jan 12, 2005 #1
    Hi all,
    when is a one-element set is linearly independent? Just when it's non-zero?
    I am not sure how to prove this on one element set.

    Thanks in advance.
  2. jcsd
  3. Jan 12, 2005 #2


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    (Assuming you speak of a vector space)

    You're right on the condition. To prove it, you need to show that if any linear combination of your one element is zero, then all the coefficients are zero.
  4. Jan 12, 2005 #3
    Ok, is that what you mean?
    S = {A},
    Code (Text):
    A = 3 3 3
        3 3 3
    A = cA?
    I do not know how to create a linear combination on one element, it doesn't make sense to me. Maybe because I started Linear Algebra course two days ago.

    Last edited: Jan 12, 2005
  5. Jan 13, 2005 #4

    matt grime

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    A linear combination of one element is just some scalar multiple of it. What is your definition of linear combination? Can't you apply it to a one element set? And what is A, it looks like an array? It is a simple exercise that if v is a non-zero vector, and tv=0 for some t in the underlying field then t=0. Which is what they're asking you to prove.
  6. Jan 14, 2005 #5
    I think I got confused linear combination and linear dependency. Now, I see the difference. Thank you for the explanations.
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