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Calculating determinant by cofactors

  1. Aug 2, 2006 #1

    Bob

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    Show that evaluating the determinant of an n*n matrix by cofactors involves (n!-1) additions and [tex]\sum^{n-1}_{k=1}n!/k![/tex]multiplications.

    What does it mean? how to do it? Help!!!
     
    Last edited: Aug 2, 2006
  2. jcsd
  3. Aug 2, 2006 #2

    matt grime

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    Induction. You're trying to count the number of basic operations in expanding this (a necessary technique if one wants to estimate how long it will take on a computer). You can do this inductively since expanding by cofactors writes an nxn determinant in terms of n lots of (n-1)x(n-1) determinants.
     
  4. Aug 3, 2006 #3

    HallsofIvy

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    As and example, to find the determinant
    [tex]\left|\begin{array}{cc}a && b \\ c && d\end{array}\right|= ad- bc[/tex]
    You must do (2!)- 1= 1 addition (ad+ (-bc)) and
    [tex]\sum^{2-1}_{k=1}2!/k= \frac{2!}{1}= 2[/tex]
    multiplications, ad and bc.
     
  5. Aug 4, 2006 #4

    Bob

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    thank you!
     
    Last edited: Aug 5, 2006
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