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(B) Let $\Delta = \left|\begin{array}{ccc} k+r & p & q \ r & k+p & q \ r & p & k+q \end{array}ight|$.Applying the operation $C_1 	o C_1 + C_2 + C

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$2k^3$

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(B) Let $\Delta = \left|\begin{array}{ccc} k+r & p & q \ r & k+p & q \ r & p & k+q \end{array}ight|$.Applying the operation $C_1 	o C_1 + C_2 + C_3$:$\Delta = \left|\begin{array}{ccc} k+p+q+r & p & q \ k+p+q+r & k+p & q \ k+p+q+r & p & k+q \end{array}ight|$.Since $k = p+q+r$,we have $k+p+q+r = 2k$.$\Delta = \left|\begin{array}{ccc} 2k & p & q \ 2k & k+p & q \ 2k & p & k+q \end{array}ight| = 2k \left|\begin{array}{ccc} 1 & p & q \ 1 & k+p & q \ 1 & p & k+q \end{array}ight|$.Applying $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_1$:$\Delta = 2k \left|\begin{array}{ccc} 1 & p & q \ 0 & k & 0 \ 0 & 0 & k \end{array}ight|$.Expanding along the first column:$\Delta = 2k 	imes (1 	imes (k^2 - 0)) = 2k 	imes k^2 = 2k^3$.

If $k = p + q + r$,then the value of $\left|\begin{array}{ccc} k+r & p & q \\ r & k+p & q \\ r & p & k+q \end{array}\right|$ is equal to:

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