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Math Help - Determinant and Linear Dependence

  1. #1
    Junior Member
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    Sep 2008
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    Freiburg i. Brgs. Germany
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    Question Determinant and Linear Dependence

    Hi,

    a 3x3 matrix with the determimant zero means that the three column vecorts are linear dependent.

    two questions about that:

    1.) Is this also correct for a 4x4 matrix?

    2.) Is this argument with the determinant if we are talking about linear dependence for all matrices valid, or only for quadratic matrices?

    Thanks
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  2. #2
    Member
    Joined
    May 2008
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    Hi!

    (1) This is valid for any nxn matrix: det(A) nonzerto iff columns, rows respectively are linearly independent.

    (2) The determinant is only defined for square matrices.
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