Let $a, b, c$ be positive and not all equal, the value of the determinant $∣ ∣ ∣ ∣ \begin{matrix} a & b & c b & c & a c & a & b \end{matrix} ∣ ∣ ∣ ∣$ , is

+ive

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-ive

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zero

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none of these

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Solution

The correct option is C -ive
Put $a = 1, b = 2, c = 3$ in the given determinant
Then, $∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ∣ ∣ ∣ ∣$
$= 1 (5) - 2 (1) + 3 (- 7) = - 18$
So, determinant value will be negative.

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