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Math Help - determinant

  1. #1
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    determinant

    I was given a question, i am to use determinants to find out if the following 3 vectors are linearly independent. The following x's are columns but im not sure how to type out columns so they are posted as rows.

    x1=7,1,5,6
    x2=5,2,4,1
    x3=2,-1,1,1

    To use determinants you need a square matrix correct? and to do that i simply added a 4th column of 0,0,0,0. This would make the determinant 0 and mean the matrix is linearly independent? This seems way to easy, as if im overlooking something.
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  2. #2
    MHF Contributor
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    Re: determinant

    If the vectors are linearly dependent, then if you select any three columns, the rows of the resulting 3 x 3 matrix will still be dependent. So, to prove linear independence, it is sufficient to find three columns so that the determinant of the resulting matrix is nonzero.
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