A) \[51\]
B) \[27\]
C) \[81\]
D) \[91\]
Correct Answer: C
Solution :
Given, \[\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|=3\] Now, \[\left| \begin{matrix} 3{{a}_{1}} & 9{{b}_{1}} & 3{{c}_{1}} \\ {{a}_{2}} & 3{{b}_{2}} & {{c}_{2}} \\ 3{{a}_{3}} & 9{{b}_{3}} & 3{{c}_{3}} \\ \end{matrix} \right|\] \[=3\times 3\left| \begin{matrix} {{a}_{1}} & 3{{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & 3{{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & 3{{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\] \[=9\times 3\left| \begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix} \right|\] \[=27\times 3=81\]
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