A) 0
B) \[m{{a}_{1}}{{a}_{2}}{{a}_{3}}\]
C) \[m{{a}_{1}}{{a}_{2}}{{b}_{3}}\]
D) \[m{{b}_{1}}{{a}_{2}}{{a}_{3}}\]
Correct Answer: A
Solution :
\[\left| \,\begin{matrix} {{a}_{1}} & m{{a}_{1}} & {{b}_{1}} \\ {{a}_{2}} & m{{a}_{2}} & {{b}_{2}} \\ {{a}_{3}} & m{{a}_{3}} & {{b}_{3}} \\ \end{matrix}\, \right|=m\,\left| \,\begin{matrix} {{a}_{1}} & {{a}_{1}} & {{b}_{1}} \\ {{a}_{2}} & {{a}_{2}} & {{b}_{2}} \\ {{a}_{3}} & {{a}_{3}} & {{b}_{3}} \\ \end{matrix}\, \right|=0\], \[\{\therefore {{C}_{1}}\equiv {{C}_{2}}\}\].
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