The largest value of a third order determinant whose elements are equa

1.	The largest value of a third order determinant whose elements are equal to `1 or 0` isA. 1B. 0C. 2D. 3
Answer» Correct Answer - C Let `Delta = \|(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3))\|` be a determinant of order 3. Then, `Delta = a_(1) b_(2) c_(3) + a_(3) b_(1) c_(2) + a_(2) b_(3) c_(1) - a_(1) b_(3) c_(2) - a_(2) b_(1) c_(3) - a_(3) b_(2) c_(1)` `Delta = (a_(1) b_(2) c_(3) + a_(3) b_(1) c_(2) + a_(2) b_(3) c_(1)) - (a_(1) b_(3) c_(2) + a_(2) b_(1) c_(3) + a_(3) b_(2) c_(1))` Since each element of `Delta` is either 1 or 0. Therefore, the value of the determinant cannot exceed 3. Clearly, the value of `Delta` is maximum when the value of each term in first bracket is 1 and the value of each term in the second bracket is zero. But `a_(1) b_(2) c_(3) = a_(3) b_(1) c_(2) = a_(2) b_(3) c_(1) = 1` implies that every element of the determinant `Delta` is 1 and in that case `Delta = 0`. Thus, we may have `Delta = \|(0,1,1),(1,0,1),(1,1,0)\| =2`

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