left|begin{array}{ccc}x & 3x+2 & 2x-1 2x-1 & | vedclass

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(D) Given the determinant: $\Delta = \left|\begin{array}{ccc}x & 3x+2 & 2x-1 \ 2x-1 & 4x & 3x+1 \ 7x-2 & 17x+6 & 12x-1\end{array}ight| = 0$.Apply

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infinitely many values of $x$

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(D) Given the determinant: $\Delta = \left|\begin{array}{ccc}x & 3x+2 & 2x-1 \ 2x-1 & 4x & 3x+1 \ 7x-2 & 17x+6 & 12x-1\end{array}ight| = 0$.Apply the row operation $R_{3} ightarrow R_{3} - 3R_{1} - 2R_{2}$:For the third row elements:$R_{3,1} = (7x-2) - 3(x) - 2(2x-1) = 7x - 2 - 3x - 4x + 2 = 0$.$R_{3,2} = (17x+6) - 3(3x+2) - 2(4x) = 17x + 6 - 9x - 6 - 8x = 0$.$R_{3,3} = (12x-1) - 3(2x-1) - 2(3x+1) = 12x - 1 - 6x + 3 - 6x - 2 = 0$.Since all elements of the third row are $0$, the value of the determinant is $0$ for all values of $x$.Therefore, the equation is true for infinitely many values of $x$.

$\left|\begin{array}{ccc}x & 3x+2 & 2x-1 \\ 2x-1 & 4x & 3x+1 \\ 7x-2 & 17x+6 & 12x-1\end{array}\right|=0$ is true for

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