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Inverse matrix in a relation

  1. Nov 5, 2006 #1
    Hi .
    I have this question( discrete math) :
    How can the matrix for R-1 , the inverse of the relation R, be found from the matrix representing R, when R is a relation a finite set A.

    How can I do this problem?
     
  2. jcsd
  3. Nov 6, 2006 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    When in doubt, try a simple example. Suppose A= {1, 2, 3} and R is defined as {(1, 1), (1, 3), (2, 3)} (I just made that up pretty much at random. Remember that a "relation on A" is just a collection of pairs of members of A.) Now, the "matrix representing R" is the matrix having 1 in the "a row, b column" when (a,b) is in R, 0 otherwise. here, labeling the rows and columns 1, 2, 3 in that order, the matrix is
    [tex]\left(\begin{array}{ccc}1 & 0 & 1\\0 & 0 &1 \\0 & 0 & 0\end{array}\right)[/tex].

    What is the relation R-1? What matrix represents it? How are the two matrices related?
     
  4. Nov 6, 2006 #3
    I think, we need to find a matrix R-1 such that R*R-1=indentity matrix
     
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