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Math Help - Verify Determinants

  1. #1
    Junior Member
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    Verify Determinants

    I need to verify that det EA = (det E)(det A)

    A = a b
    ......c d

    E = 1 0
    ......K 1

    I got -b(kb +d) for det EA. but for (det E)(det A) I get ad - cb - k(ad-cb)

    I'm not sure at what point I am screwing this up at. TIA!!!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by TreeMoney View Post
    I need to verify that det EA = (det E)(det A)

    A = a b
    ......c d

    E = 1 0
    ......K 1

    I got -b(kb +d) for det EA. but for (det E)(det A) I get ad - cb - k(ad-cb)

    I'm not sure at what point I am screwing this up at. TIA!!!
    EA = [...a....b...]
    .......[ka+c.kb+d]

    so det(EA) = a(kb+d) - b(ka+c) = ad - bc,

    also det(E) = 1, det(A) = ad - bc,

    so we have det(EA) = det(E) det(A).

    RonL
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