Let $$\Delta =\left| \begin{matrix} 1+{{x}_{1}}{{y}_{1}} & 1+{{x}_{1}}{{y}_{2}} & 1+{{x}_{1}}{{y}_{3}} \ 1+{{x}_{2}}{{y}_{1}} & 1+{{x}_{2}}{{y}_{2}} & \,1+{{x}_{2}}{{y}_{3}} \ 1+{{x}_{3}}{{y}_{1}} & 1+{{x}_{3}}{{y}_{2}} & 1+{{x}_{3}}{{y}_{3}} \ \end{matrix} \right|$$ then value of $$\Delta $$ is

Question

Let $$\Delta =\left| \begin{matrix}    1+{{x}_{1}}{{y}_{1}} & 1+{{x}_{1}}{{y}_{2}} & 1+{{x}_{1}}{{y}_{3}}  \    1+{{x}_{2}}{{y}_{1}} & 1+{{x}_{2}}{{y}_{2}} & \,1+{{x}_{2}}{{y}_{3}}  \    1+{{x}_{3}}{{y}_{1}} & 1+{{x}_{3}}{{y}_{2}} & 1+{{x}_{3}}{{y}_{3}}  \ \end{matrix} \right|$$ then value of $$\Delta $$ is

TuteeHUB · Accepted Answer

NA

TuteeHUB · Answer

$${{x}_{1}}{{x}_{2}}{{x}_{3}}+{{y}_{1}}{{y}_{2}}{{y}_{3}}$$

TuteeHUB · Answer

$${{x}_{1}}{{x}_{2}}{{x}_{3}}{{y}_{1}}{{y}_{2}}{{y}_{3}}$$

TuteeHUB · Answer

$${{x}_{2}}{{x}_{3}}{{y}_{2}}{{y}_{3}}+{{x}_{3}}{{x}_{1}}{{y}_{3}}{{y}_{1}}+{{x}_{1}}{{x}_{2}}{{y}_{1}}{{y}_{2}}$$

1.	Let \[\Delta =\left\| \begin{matrix} 1+{{x}_{1}}{{y}_{1}} & 1+{{x}_{1}}{{y}_{2}} & 1+{{x}_{1}}{{y}_{3}} \\ 1+{{x}_{2}}{{y}_{1}} & 1+{{x}_{2}}{{y}_{2}} & \,1+{{x}_{2}}{{y}_{3}} \\ 1+{{x}_{3}}{{y}_{1}} & 1+{{x}_{3}}{{y}_{2}} & 1+{{x}_{3}}{{y}_{3}} \\ \end{matrix} \right\|\] then value of \[\Delta \] is
A.	\[{{x}_{1}}{{x}_{2}}{{x}_{3}}+{{y}_{1}}{{y}_{2}}{{y}_{3}}\]
B.	\[{{x}_{1}}{{x}_{2}}{{x}_{3}}{{y}_{1}}{{y}_{2}}{{y}_{3}}\]
C.	\[{{x}_{2}}{{x}_{3}}{{y}_{2}}{{y}_{3}}+{{x}_{3}}{{x}_{1}}{{y}_{3}}{{y}_{1}}+{{x}_{1}}{{x}_{2}}{{y}_{1}}{{y}_{2}}\]
D.	0
Answer» E.

Let \[\Delta =\left| \begin{matrix} 1+{{x}_{1}}{{y}_{1}} & 1+{{x}_{1}}{{y}_{2}} & 1+{{x}_{1}}{{y}_{3}} \\ 1+{{x}_{2}}{{y}_{1}} & 1+{{x}_{2}}{{y}_{2}} & \,1+{{x}_{2}}{{y}_{3}} \\ 1+{{x}_{3}}{{y}_{1}} & 1+{{x}_{3}}{{y}_{2}} & 1+{{x}_{3}}{{y}_{3}} \\ \end{matrix} \right|\] then value of \[\Delta \] is

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