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Math Help - Question: vectors-linearly independent for any value of k

  1. #1
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    Question: vectors-linearly independent for any value of k

    Can anyone help me solve this question with workings:

    1. Can u= [1,2,-1], v=[2,k2,k] be linearly independent for any k?

    Thanks, would really appreciate any help-it is my last question and I'm stuck.
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  2. #2
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    Re: Question: vectors-linearly independent for any value of k

    Two vectors are linearly independent if one is not a scalar multiple of the other. To be more precise, two vectors are linearly independent if and only if the matrix A = [u v] whose columns are the vectors u and v has exactly 2 pivots.
    Thanks from tbea009
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