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Question

Find the maximum value of 3×3 determinant whose elements are 0,1.


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Solution

Identify the determinants and its maximum value

Case I: If all the entries in one row are 0, then the value of the determinants is 0.

For example D=000101110=0
Case II: If all the entries in one row are 1 and non of the rows having all entries 0, then the maximum value of determinant is 1.

Case III: If exactly one 1 is in each one row, then the maximum value is 1.
Case IV: If exactly two 1 is in one row, then the maximum value is 2.

For example D=011101110=00110-11110+11011=0+1+1=2

Hence, the largest value of the determinant with entries either 0 or 1 is 2.


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