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Math Help - determinant and adujagate

  1. #1
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    determinant and adujagate

    If A is 3x3 matrix and detA = 2

    det((A^(-1)) + 4adj4)

    i understand how to do stuff with determinants if i had a fuction before but this don't really understand and i know i cant add the 2 determinants,

    thanks.

    p.s. I tried to write it in latex but the ^-1 wouldn't work it would only put the negative sign in superscript

    alright so i know that A^-1 = adj(A)det(A)^-1


    so by this

    det(A^-1 + 4(A^-1)(detA)) since detA = 2
    det(A^-1 + 8A^-1)
    det(9A^-1) since I = A(A^-1) since A has an inverse we know its invertible and this is true
    9Det(I)
    ------- = 9/2
    Det(A)

    can someone verify that my algebra is correct cus I'm not too sure
    Last edited by treetheta; December 10th 2009 at 08:39 PM.
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  2. #2
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    Quote Originally Posted by treetheta View Post
    If A is 3x3 matrix and detA = 2

    det((A^(-1)) + 4adj4)

    i understand how to do stuff with determinants if i had a fuction before but this don't really understand and i know i cant add the 2 determinants,

    thanks.

    p.s. I tried to write it in latex but the ^-1 wouldn't work it would only put the negative sign in superscript

    alright so i know that A^-1 = adj(A)det(A)^-1


    so by this

    det(A^-1 + 4(A^-1)(detA)) since detA = 2
    det(A^-1 + 8A^-1)
    det(9A^-1) since I = A(A^-1) since A has an inverse we know its invertible and this is true
    9Det(I)
    ------- = 9/2
    Det(A)

    can someone verify that my algebra is correct cus I'm not too sure
    You are right if you meant "det(A^-1 + 4Adj A)"
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