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Math Help - Question : Determinants

  1. #1
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    Smile Question : Determinants

    Hi please anyone help me with this question, its a combination of Permutations&Combinations and Determinants.

    Q. There is a 3X3 determinant in which each element is either 1 or 0. It is given that aij = aji . There are total seven 1s in this determinants. How many such Determinants are possible?

    (Answer : 6 )
    Please give me an easy solution.
    Thanks
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    Quote Originally Posted by enigmaticfire View Post
    Hi please anyone help me with this question, its a combination of Permutations&Combinations and Determinants.

    Q. There is a 3X3 determinant in which each element is either 1 or 0. It is given that aij = aji . There are total seven 1s in this determinants. How many such Determinants are possible?

    (Answer : 6 )
    There are nine elements in a 3x3 matrix: three on the main diagonal, and three pairs of off-diagonal elements. The condition a_{ij} = a_{ji} says that the two elements in each off-diagonal pair are equal. If seven of the elements are 1 then only two elements are 0. There are two ways in which that can happen. Either the two elements in one of the off-diagonal pairs are both 0, or two of the elements on the diagonal are 0. Count the number of ways in which each of these possibilities can occur.
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