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Math Help - calculate matrices

  1. #1
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    calculate matrices

    Please help, I searched the text several times but could not figure out how to solve this problem

    How many 6 x 6 (0, 1)-matrices A are there with A = A^tr?
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  2. #2
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    Re: calculate matrices

    Maybe you can find first how many symmetric 2 x 2 and 3 x 3 (0, 1)-matrices there are.
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  3. #3
    Member kalyanram's Avatar
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    Re: calculate matrices

    Quote Originally Posted by wattskickin View Post
    Please help, I searched the text several times but could not figure out how to solve this problem

    How many 6 x 6 (0, 1)-matrices A are there with A =A^tr?
    I hope this is what you mean.
    How many 6x6 matrices A can be there such that A = A^T. Elements of the matrices can be selected from the set \{0,1\}?

    Sol: For A=A^T we need a_{ij} = a_{ji} where a_{ij} is the element in the i^{th} row j^{th} column.
    We consider the elements a_{ij} where i \le j(why ?). There are 21 such elements and for each of these elements we have 2 choices so we have 2^{21} such matrices.

    Kalyan.
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