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Linearly Independent

  1. Feb 27, 2010 #1
    Let x1, x2,...,xk be linear independent vectors in a vector space V.

    If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain.

    By deleting a vector from linearly independent span, the other vectors will remain independent; however, I don't know how to prove it.
  2. jcsd
  3. Feb 27, 2010 #2
    So delete one, say v_i. If the remaining vectors are linearly dependent, then there exist scalars for which the linear combination of the remaining vectors equals 0. What happens when you add 0*(v_i) to both sides?
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