A) \[\left[ \begin{matrix} \frac{4}{14} & \frac{2}{14} \\ \frac{-1}{14} & \frac{3}{14} \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} \frac{3}{14} & \frac{-2}{14} \\ \frac{1}{14} & \frac{4}{14} \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} \frac{4}{14} & \frac{-2}{14} \\ \frac{1}{14} & \frac{3}{14} \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} \frac{3}{14} & \frac{2}{14} \\ \frac{1}{14} & \frac{4}{14} \\ \end{matrix} \right]\]
Correct Answer: A
Solution :
Let \[A=\left[ \begin{matrix} 3 & -2 \\ 1 & 4 \\ \end{matrix} \right]\,\Rightarrow |A|=14\] \[\therefore \] \[adj\,A=\left[ \begin{matrix} 4 & 2 \\ -1 & 3 \\ \end{matrix} \right]\] \[\Rightarrow \] \[{{A}^{-1}}=\left[ \begin{matrix} \frac{4}{14} & \frac{2}{14} \\ \frac{-1}{14} & \frac{3}{14} \\ \end{matrix} \right]\].You need to login to perform this action.
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