A) \[\left| \,\begin{matrix} 2 & -5 & 7 \\ 1 & 1 & 6 \\ 3 & 2 & 1 \\ \end{matrix}\, \right|\div \left| \,\begin{matrix} 7 & 3 & -5 \\ 6 & 1 & 1 \\ 1 & -4 & 2 \\ \end{matrix}\, \right|\]
B) \[\left| \,\begin{matrix} -7 & 3 & -5 \\ -6 & 1 & 1 \\ -1 & -4 & 2 \\ \end{matrix}\, \right|\div \left| \,\begin{matrix} 2 & 3 & -5 \\ 1 & 1 & 1 \\ 3 & -4 & 2 \\ \end{matrix}\, \right|\]
C) \[\left| \,\begin{matrix} 7 & 3 & -5 \\ 6 & 1 & 1 \\ 1 & -4 & 2 \\ \end{matrix}\, \right|\div \left| \,\begin{matrix} 2 & 3 & -5 \\ 1 & 1 & 1 \\ 3 & -4 & 2 \\ \end{matrix}\, \right|\]
D) None of these
Correct Answer: C
Solution :
For the given set of equation, by Cramer?s Rule \[x=\frac{{{D}_{x}}}{D}=\left| \,\begin{matrix} 7 & \,\,3 & -5 \\ 6 & \,\,1 & \,\,1 \\ 1 & -4 & \,\,2 \\ \end{matrix}\, \right|\,\div \left| \,\begin{matrix} 2 & \,\,3 & -5 \\ 1 & \,\,1 & \,\,1 \\ 3 & -4 & \,\,2 \\ \end{matrix}\, \right|\].
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