A) 2
B) 3
C) \[-4\]
D) 4
E) \[-2\]
Correct Answer: D
Solution :
Given matrix is \[A=\left[ \begin{matrix} x & -2 \\ 3 & 7 \\ \end{matrix} \right]\] \[\therefore \] \[|A|=7x+6\] \[\therefore \] \[{{A}^{-1}}=\left[ \begin{matrix} \frac{7}{7x+6} & \frac{2}{7x+6} \\ \frac{-3}{7x+6} & \frac{x}{7x+6} \\ \end{matrix} \right]\] Comparing it with given inverse matrix \[{{A}^{-1}}=\left[ \begin{matrix} \frac{7}{34} & \frac{1}{17} \\ \frac{-3}{24} & \frac{2}{17} \\ \end{matrix} \right],\] we get \[\frac{7}{7x+6}=\frac{7}{34}\] \[\Rightarrow \] \[x=4\]
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