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Math Help - how to tell if determinant is negative or positve of 4x4 matrix

  1. #1
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    how to tell if determinant is negative or positve of 4x4 matrix

    2,3-1,1
    -1,0,1,1
    2,1,3,-2
    1,1,1,-1



    Is there any way of quickly determining this?
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  2. #2
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    No. Row reductions will tell you soon, but I wouldn't call it "quickly".
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  3. #3
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by lord12 View Post
    2,3-1,1
    -1,0,1,1
    2,1,3,-2
    1,1,1,-1



    Is there any way of quickly determining this?
    use expansion method:

    det (A) = a_{i1}A_{i1} + a_{i2}A_{i2} + ... + a_{in}A_{in}
    this is expansion about the ith row..
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  4. #4
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    Also, "no". Certainly, it can be determined using a few methods.
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