For non-zero a, b, c,if Delta = begin{vmatrix | vedclass

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(D) Given $\Delta = \begin{vmatrix} 1 + a & 1 & 1 \ 1 & 1 + b & 1 \ 1 & 1 & 1 + c \end{vmatrix} = 0$.Taking $a, b, c$ common from $C_1, C_2, C_3$ re

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$-1$

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(D) Given $\Delta = \begin{vmatrix} 1 + a & 1 & 1 \ 1 & 1 + b & 1 \ 1 & 1 & 1 + c \end{vmatrix} = 0$.Taking $a, b, c$ common from $C_1, C_2, C_3$ respectively:$\Delta = abc \begin{vmatrix} \frac{1}{a} + 1 & \frac{1}{b} & \frac{1}{c} \ \frac{1}{a} & \frac{1}{b} + 1 & \frac{1}{c} \ \frac{1}{a} & \frac{1}{b} & \frac{1}{c} + 1 \end{vmatrix}$.Applying $C_1 	o C_1 + C_2 + C_3$:$\Delta = abc \begin{vmatrix} 1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} & \frac{1}{b} & \frac{1}{c} \ 1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} & \frac{1}{b} + 1 & \frac{1}{c} \ 1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} & \frac{1}{b} & \frac{1}{c} + 1 \end{vmatrix}$.Taking $(1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c})$ common from $C_1$:$\Delta = abc (1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c}) \begin{vmatrix} 1 & \frac{1}{b} & \frac{1}{c} \ 1 & \frac{1}{b} + 1 & \frac{1}{c} \ 1 & \frac{1}{b} & \frac{1}{c} + 1 \end{vmatrix}$.Applying $R_2 	o R_2 - R_1$ and $R_3 	o R_3 - R_1$:$\Delta = abc (1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c}) \begin{vmatrix} 1 & \frac{1}{b} & \frac{1}{c} \ 0 & 1 & 0 \ 0 & 0 & 1 \end{vmatrix}$.Expanding along $C_1$,we get $\Delta = abc (1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c}) 	imes 1 = 0$.Since $a, b, c 
eq 0$,$abc 
eq 0$. Therefore,$1 + \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 0$,which implies $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = -1$.

For non-zero $a, b, c$,if $\Delta = \begin{vmatrix} 1 + a & 1 & 1 \\ 1 & 1 + b & 1 \\ 1 & 1 & 1 + c \end{vmatrix} = 0$,then the value of $\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = $

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