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Question

If the entries in a 3×3 determinant are either 0 or 1, then the greatest value of their determinats is:

A
1
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B
2
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C
3
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D
9
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Solution

The correct option is C 2
Case I: If all the entries in one row are 0 , then the determinant is 0.
Case II: If all the entries in one row are 1 , then the maximum value of determinant is 1.
111011101
Case II:If exactly one 1 is in one row, then the maximum value is 1.
100010001
Case III:If exactly two 1 is in one row, then the maximum value is 2.
110011101
Hence, the largest value of the determinant with entries either 0 or 1 is 2.

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