The value of left|begin{array}{lll}x & p & q | vedclass

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(A) Let $\Delta = \left|\begin{array}{lll}x & p & q \ p & x & q \ p & q & x\end{array}ight|$.Applying $R_1 	o R_1 - R_2$:$\Delta = \left|\begin{a

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$(x-p)(x-q)(x+p+q)$

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(A) Let $\Delta = \left|\begin{array}{lll}x & p & q \ p & x & q \ p & q & x\end{array}ight|$.Applying $R_1 	o R_1 - R_2$:$\Delta = \left|\begin{array}{lll}x-p & p-x & 0 \ p & x & q \ p & q & x\end{array}ight| = (x-p) \left|\begin{array}{lll}1 & -1 & 0 \ p & x & q \ p & q & x\end{array}ight|$.Applying $C_2 	o C_2 + C_1$:$\Delta = (x-p) \left|\begin{array}{lll}1 & 0 & 0 \ p & x+p & q \ p & q+p & x\end{array}ight|$.Expanding along $R_1$:$\Delta = (x-p) [1 \cdot ((x+p)x - q(q+p)) - 0 + 0]$$\Delta = (x-p) [x^2 + xp - q^2 - qp]$$\Delta = (x-p) [x^2 - q^2 + xp - qp]$$\Delta = (x-p) [(x-q)(x+q) + p(x-q)]$$\Delta = (x-p)(x-q)(x+q+p)$.

The value of $\left|\begin{array}{lll}x & p & q \\ p & x & q \\ p & q & x\end{array}\right|$ is

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