A) \[-3\]
B) \[3\]
C) \[-2\]
D) \[6\]
E) \[-6\]
Correct Answer: A
Solution :
\[A=\left[ \begin{matrix} 2 & 1 \\ 0 & x \\ \end{matrix} \right]{{A}^{-1}}=\left[ \begin{matrix} 1/2 & 1/6 \\ 0 & 1/x \\ \end{matrix} \right]\] \[\Rightarrow \] \[|A|=2x\] And adj \[(A)=\left[ \begin{matrix} x & -1 \\ 0 & 2 \\ \end{matrix} \right]\] Now, \[{{A}^{-1}}=\frac{adj(A)}{|A|}\] \[\Rightarrow \] \[\left[ \begin{matrix} 1/2 & 1/6 \\ 0 & 1/x \\ \end{matrix} \right]=\frac{1}{2x}\left[ \begin{matrix} x & -1 \\ 0 & 2 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 1/2 & -1/2x \\ 0 & 1/x \\ \end{matrix} \right]\] On comparing, \[-1/2x=1/6\] \[\Rightarrow \] \[x=-3\]You need to login to perform this action.
You will be redirected in
3 sec