Question

$\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 7 x-2 & 17 x+6 & 12 x-1\end{array}\right|=0$ is true for
(A) only one value of $x$
(B) only two values of $x$
(C) only three values of $x$
(D) infinitely many values of $x$

Answer 1

Ans: (D)
Hint : $\left|\begin{array}{ccc}x & 3 x+2 & 2 x-1 \\ 2 x-1 & 4 x & 3 x+1 \\ 7 x-2 & 17 x+6 & 12 x-1\end{array}\right|=0$
$$\begin{aligned} &\mathrm{R}_{3} \rightarrow \mathrm{R}_{3}-3 \mathrm{R}_{1}-2 \mathrm{R}_{2} \\ &\left|\begin{array}{ccc} \mathrm{x} & 3 \mathrm{x}+2 & 2 \mathrm{x}-1 \\ 2 \mathrm{x}-1 & 4 \mathrm{x} & 3 \mathrm{x}+1 \\ 0 & 0 & 0 \end{array}\right|=0 \end{aligned}$$
Infinite values of $x$ is possible.

Answer 2

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Answer 3

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