Consider the system of linear equations a_1x | vedclass

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(B) The given system of linear equations is:$a_1x + b_1y + c_1z = -d_1$$a_2x + b_2y + c_2z = -d_2$$a_3x + b_3y + c_3z = -d_3$According to Cramer's rul

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$\frac{-\Delta (bcd)}{\Delta (abc)}$

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(B) The given system of linear equations is:$a_1x + b_1y + c_1z = -d_1$$a_2x + b_2y + c_2z = -d_2$$a_3x + b_3y + c_3z = -d_3$According to Cramer's rule,the value of $x$ is given by $x = \frac{D_x}{D}$,where $D = \Delta (a,b,c) = \begin{vmatrix} a_1 & b_1 & c_1 \ a_2 & b_2 & c_2 \ a_3 & b_3 & c_3 \end{vmatrix}$ and $D_x = \begin{vmatrix} -d_1 & b_1 & c_1 \ -d_2 & b_2 & c_2 \ -d_3 & b_3 & c_3 \end{vmatrix}$.Taking $-1$ common from the first column of $D_x$,we get:$D_x = -1 	imes \begin{vmatrix} d_1 & b_1 & c_1 \ d_2 & b_2 & c_2 \ d_3 & b_3 & c_3 \end{vmatrix} = -\Delta (d,b,c) = -\Delta (b,c,d)$.Thus,$x = \frac{-\Delta (bcd)}{\Delta (abc)}$.

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