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Homework Help: Proof of Linearly independence

  1. Sep 21, 2012 #1
    The problem is attached. I just wanted to see if the way I proved my statement is correct.

    My answer: No, because there exists more columns than rows, thus at least one free variable always exists, thus these vectors are linearly dependent.

    Attached Files:

  2. jcsd
  3. Sep 21, 2012 #2


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    You are right but, personally, I wouldn't phrase it in terms of "columns" and "rows" since nothing is said of matrices in the problem. Rather, I would not that Rm has dimension m so there is a basis containing m vectors. Every one of the n vectors in the set can be written in terms of the the m vectors in the basis so they cannot be independent.

    (A basis for an m-dimensional vector space has three properties:
    1) they span the space
    2) they are independent
    3) there are m vectors in the set
    Any set containing fewer than m vectors cannot span the space, any set with more than m vectors cannot be independent.)
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