question_answer

Suppose \[D=\left| \,\begin{matrix}    {{a}_{1}} & {{b}_{1}} & {{c}_{1}}  \\    {{a}_{2}} & {{b}_{2}} & {{c}_{2}}  \\    {{a}_{3}} & {{b}_{3}} & {{c}_{3}}  \\ \end{matrix}\, \right|\]and     \[{D}'=\left| \,\begin{matrix}    {{a}_{1}}+p{{b}_{1}} & {{b}_{1}}+q{{c}_{1}} & {{c}_{1}}+r{{a}_{1}}  \\    {{a}_{2}}+p{{b}_{2}} & {{b}_{2}}+q{{c}_{2}} & {{c}_{2}}+r{{a}_{2}}  \\    {{a}_{3}}+p{{b}_{3}} & {{b}_{3}}+q{{c}_{3}} & {{c}_{3}}+r{{a}_{3}}  \\ \end{matrix}\, \right|\], then [Karnataka CET 1993; Pb. CET 1993]

A) \[{D}'=D\]

B) \[{D}'=D(1-pqr)\]

C) \[{D}'=D(1+p+q+r)\]

D) \[{D}'=D(1+pqr)\]