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Math Help - Vector

  1. #1
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    Vector

    How are the 2 vectors linearly dependent or linearly independent?

    The question is

    Examine whether the vector i-j+2k,2i+j-3k, 2i-5j+k are linearly independent or linearly dependent?
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  2. #2
    Senior Member DeMath's Avatar
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    Examine whether the vector i-j+2k,2i+j-3k, 2i-5j+k are linearly independent or linearly dependent?
    You need compose a determinant from the coordinates of these vectors.
    If a determinant is equal to 0, then vectors are linearly dependent, and conversely, vectors are linearly independent if a determinant is not equal to 0.

    For your problem  i-j+2k, 2i+j-3k, 2i-5j+k it must be \left| {\begin{array}{*{20}{c}}1 & { - 1} & 2  \\2 & 1 & { - 3}  \\2 & { - 5} & 1  \\\end{array} } \right|.
    Last edited by DeMath; January 10th 2009 at 04:23 AM.
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