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Homework Help: Adjugate of A

  1. Dec 7, 2013 #1
    I need to find the adj(A) for a 4x4 Matrix.

    [tex]A = \begin{array} a11 & a12 & a13 & a14 \\ a21 & a22 & a23 & a24 \\ a31 & a32 & a33 & a34 \\ a41 & a42 & a43 & a44 \end{array}[/tex]

    I have tried:

    [tex]adj(A_{ij}) = (-1)^{i+j}*A_{ji}[/tex]

    but I get the wrong answer for the inverse:

    [tex]A^{-1} = \frac{adj(A)}{det(A)}[/tex]

    and this does not work:

    [tex]A*A^{-1} = I[/tex]

    where

    [tex]I= \begin{array} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{array}[/tex]
     
  2. jcsd
  3. Dec 8, 2013 #2

    Simon Bridge

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    Science Advisor
    Homework Helper

    ##C_{ij}=(-1)^{i+j}A_{ij}## ... gives you ##\text{C}## - the cofactor matrix.
    The adjugate matrix is the transpose of the cofactor matrix.
     
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