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Det of a matrix

  1. Aug 9, 2005 #1
    could someone please explain simply how to get the determinate of a 3 * 3 matrix i'm relly stuck i've looked through my text books but it only has examples of how to do it useing a grapgics calculator thanks
     
  2. jcsd
  3. Aug 9, 2005 #2
    you break it up into three 2x2 determinents!

    http://mathworld.wolfram.com/Determinant.html

    look at the first line of eqt. 27
     
  4. Aug 9, 2005 #3

    TD

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    Homework Helper

    You could do that, or use some properties first to create 0's and then develop to a row or column. There's also a direct way, but it's a bit 'long':

    [tex]\begin{gathered}
    A = \left( {\begin{array}{*{20}c}
    {a_{11} } & {a_{12} } & {a_{13} } \\
    {a_{21} } & {a_{22} } & {a_{23} } \\
    {a_{31} } & {a_{32} } & {a_{33} } \\
    \end{array} } \right) \Rightarrow \det \left( A \right) = \left| {\begin{array}{*{20}c}
    {a_{11} } & {a_{12} } & {a_{13} } \\
    {a_{21} } & {a_{22} } & {a_{23} } \\
    {a_{31} } & {a_{32} } & {a_{33} } \\
    \end{array} } \right| \hfill \\ \\
    = a_{1,1}\cdot{a}_{2,2}\cdot{a}_{3,3} + a_{1,3}\cdot{a}_{3,2}\cdot{a}_{2,1} + a_{1,2}\cdot{a}_{2,3}\cdot{a}_{3,1} -
    a_{1,3}\cdot{a}_{2,2}\cdot{a}_{3,1} - a_{1,1}\cdot{a}_{2,3}\cdot{a}_{3,2} - a_{1,2}\cdot{a}_{2,1}\cdot{a}_{3,3} \hfill \\
    \end{gathered} [/tex]
     
  5. Aug 9, 2005 #4
    form Spunky_Dunkey

    thanks very much :smile:
     
  6. Aug 9, 2005 #5


    oh, right. that crap.

    :tongue:


    my calc III prof went over that, mainly as a curiosity. i've used expansion by minors exclusively.


    whatever's easiest to you!
     
  7. Aug 10, 2005 #6

    TD

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    I usually expand by minors too, but not before I simplified it first using elementary operations. Having to expand it 'in full' is long too hehe :wink:
     
  8. Aug 10, 2005 #7

    HallsofIvy

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    If you row-reduce the matrix to triangular form, finding the determinant is just multiplying the numbers on the diagonal.
     
  9. Aug 10, 2005 #8
    that's a really good idea. would have really come in handy when i was in 11th grade. :frown: (we had the occasional 4x4 determinant! :yuck: )
     
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