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Math Help - Linear dependence

  1. #1
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    Linear dependence

    Let u and v be distinct vectors in a vector space V show that {u,v} is linearly dependant if and only if u or v is a multiple of the other.


    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Matharch View Post
    Let u and v be distinct vectors in a vector space V show that {u,v} is linearly dependant if and only if u or v is a multiple of the other.


    Thanks in advance.
    A set of vectors are linearly dependent if vectors v_1 , v_2, ... v_n satisfy a_1 v_1 + a_2 v_2 + ...a_n v_n=0 where a_i is a scalar and the set of scalars are not all 0.

    So applying this to your problem, you have two vectors. Assume that they are linearly dependent then apply the definition and you can easily show u or v is a multiple of the other. Then assume one is a multiple of the other and show that when this is true the two vectors satisfy the definition of lin. dep.
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  3. #3
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    Thank you very much that's what I thought but I wasn't sure.
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