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Math Help - determinat value

  1. #1
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    determinat value

    if A is symmetric matrix of odd order and aii=0 for all i then prove that determinant of A is an even number.

    please explain.
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  2. #2
    Super Member girdav's Avatar
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    Re: determinat value

    Has the matrix real entries?
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    Re: determinat value

    yes, the entries are integers, other than diagonal elements.
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  4. #4
    Super Member girdav's Avatar
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    Re: determinat value

    We can use the definition of the determinant. Since a_{ii}=0, we can sum over the permutations without fixed point. Since these permutations act over a set which have an odd number of elements, these one have a square different from the identity. So you can write the sum as two equal parts, which will give an even number.
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