The Largest Value Of A Third Order Determinant Whose Elements Are 0 Or 1, Is

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Question

The largest value of a third order determinant whose elements are 0 or 1, is

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Solution

Correct option is

Since each elements of âˆ† is either 1 or 0, therefore the value of the determinant cannot exceed 3. Clearly, the value of âˆ† 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 a₁ b₂c₃ = a₃ b₁ c₂ = a₂ b₃ c₁= 1 implies that every element of the determinant âˆ† is 1 and in that case âˆ† = 0. Thus, we may have