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Homework Help: How do you find the adjoint of a 3x3 matrix? can u explain example?

  1. Oct 15, 2005 #1
    Hello everyone, I think i don't understand the inverses because i don't understand how u find the adjoint of a nxn matrix. The book has this example and i have no idea how they got from A to A adj, makes no sense to me!

    Here is the picture:
    http://img89.imageshack.us/img89/3010/lastscan0oo.jpg [Broken]
    if that link is slow try:L
    http://show.imagehosting.us/show/806170/0/nouser_806/T0_-1_806170.jpg
    thanks! :biggrin:
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 15, 2005 #2
    To find the adjoint of a A:

    [tex]
    adj(A)_{ij} = (-1)^{i+j} det[A(j|i)]
    [/tex]

    That means that the entry in the row [tex]i[/tex] and column [tex]j[/tex] of [tex]adj(A)[/tex] is obtained by deleting the column [tex]j[/tex] and the row [tex]i[/tex] of A and then taking the determinant of that and multipliying by [tex](-1)^{i+j}[/tex]

    For instance if u have a 3x3 matrix:
    http://en.wikipedia.org/math/e36e0138b126ebbcf8fe80cd4f58f3aa.png [Broken]

    this is the adjoint:
    http://en.wikipedia.org/math/a3c81ad8680add569a7377cda2529147.png [Broken]
     
    Last edited by a moderator: May 2, 2017
  4. Oct 16, 2005 #3
    Ahh thank u so much!
     
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