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(B) Let $\Delta = \left| \begin{array}{ccc} y + z & x & y \ z + x & z & x \ x + y & y & z \end{array} ight|$.Applying $R_1 	o R_1 + R_2 + R_3$,we

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(B) Let $\Delta = \left| \begin{array}{ccc} y + z & x & y \ z + x & z & x \ x + y & y & z \end{array} ight|$.Applying $R_1 	o R_1 + R_2 + R_3$,we get:$\Delta = \left| \begin{array}{ccc} 2(x + y + z) & x + y + z & x + y + z \ z + x & z & x \ x + y & y & z \end{array} ight|$$= (x + y + z) \left| \begin{array}{ccc} 2 & 1 & 1 \ z + x & z & x \ x + y & y & z \end{array} ight|$.Applying $C_1 	o C_1 - C_2$ and $C_2 	o C_2 - C_3$:$= (x + y + z) \left| \begin{array}{ccc} 1 & 0 & 1 \ x - z & z - x & x \ x - y & y - z & z \end{array} ight|$$= (x + y + z) [1((z - x)z - x(y - z)) + 1((x - z)(y - z) - (x - y)(z - x))]$.Simplifying the expression,we get $\Delta = (x + y + z)(x - z)^2$.Comparing this with $k(x + y + z)(x - z)^2$,we find $k = 1$.

If $\left| \begin{array}{ccc} y + z & x & y \\ z + x & z & x \\ x + y & y & z \end{array} \right| = k(x + y + z)(x - z)^2$,then $k = $

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