If $|\begin{array}{lll} 2 3 2 \\ x x x \\ 4 9 1 \end{array}| + 3 = 0$ , then the value of x is

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answer is C.

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Detailed Solution

$|\begin{array}{lll} 2 3 2 \\ x x x \\ 4 9 1 \end{array}| + 3 = 0$ On expanding along R₁

$\begin{array}{l} 2 (x - 9 x) - 3 (x - 4 x) + 2 (9 x - 4 x) + 3 = 0 \\ 2 (- 8 x) - 3 (- 3 x) + 2 (5 x) + 3 = 0 \\ - 16 x + 9 x + 10 x + 3 = 0 \\ 3 x + 3 = 0 \\ \begin{aligned} 3 x = - 3 \\ x = - \frac{3}{3} \\ x = - 1 \end{aligned} \end{array}$

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