A) \[\Delta \]
B) \[{{\Delta }^{2}}\]
C) \[{{\Delta }^{3}}\]
D) 0
Correct Answer: B
Solution :
We know that \[\Delta \,{\Delta }'=\left| \,\begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix}\, \right|.\left| \,\begin{matrix} {{A}_{1}} & {{B}_{1}} & {{C}_{1}} \\ {{A}_{2}} & {{B}_{2}} & {{C}_{2}} \\ {{A}_{3}} & {{B}_{3}} & {{C}_{3}} \\ \end{matrix}\, \right|\] \[=\left| \,\begin{matrix} \Sigma {{a}_{1}}{{A}_{1}} & 0 & 0 \\ 0 & \Sigma {{a}_{2}}{{A}_{2}} & 0 \\ 0 & 0 & \Sigma {{a}_{3}}{{A}_{3}} \\ \end{matrix}\, \right|=\left| \,\begin{matrix} \Delta & 0 & 0 \\ 0 & \Delta & 0 \\ 0 & 0 & \Delta \\ \end{matrix}\, \right|={{\Delta }^{3}}\] Þ \[{\Delta }'={{\Delta }^{2}}\].
You need to login to perform this action.
You will be redirected in
3 sec
