The number of real values of x satisfying lef | vedclass

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(C) Let the determinant be $\Delta$. We perform the row operation $R_3 \rightarrow R_3 - (2R_2 + 3R_1)$.First,calculate the elements of $R_3$ after th

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more than $3$

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(C) Let the determinant be $\Delta$. We perform the row operation $R_3 \rightarrow R_3 - (2R_2 + 3R_1)$.First,calculate the elements of $R_3$ after the operation:For the first column: $(7x - 2) - [2(2x - 1) + 3(x)] = 7x - 2 - (4x - 2 + 3x) = 7x - 2 - 7x + 2 = 0$.For the second column: $(17x + 6) - [2(4x) + 3(3x + 2)] = 17x + 6 - (8x + 9x + 6) = 17x + 6 - 17x - 6 = 0$.For the third column: $(12x - 1) - [2(3x + 1) + 3(2x - 1)] = 12x - 1 - (6x + 2 + 6x - 3) = 12x - 1 - (12x - 1) = 0$.Since all elements of the third row are $0$,the value of the determinant is $0$ for all real values of $x$.Therefore,there are infinitely many real values of $x$ that satisfy the equation.Since the options provided do not include 'infinitely many',and the question asks for the number of real values,we re-evaluate the context. Given the structure,the equation holds for any $x \in \mathbb{R}$. However,if we must choose from the options,the question might be flawed or implying a specific constraint not listed. Given the mathematical result,the number of values is infinite,which is 'more than $3$'.

The number of real values of $x$ satisfying $\left| \begin{array}{ccc} x & 3x + 2 & 2x - 1 \\ 2x - 1 & 4x & 3x + 1 \\ 7x - 2 & 17x + 6 & 12x - 1 \end{array} \right| = 0$ is

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