A) [5 7]
B) \[\frac{1}{3}\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\]
C) \[\frac{1}{3}[5\,\,7]\]
D) \[\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\]
Correct Answer: B
Solution :
\[A=\left[ \,\begin{matrix} -1 & 2 \\ 2 & -1 \\ \end{matrix}\, \right]\,\,,\,\,\,B=\left[ \begin{align} & 3 \\ & 1 \\ \end{align} \right]\] \[AX=B\,\Rightarrow X={{A}^{-1}}B\] \[{{A}^{-1}}=\frac{adj\,A}{|A|}\] \[{{A}^{-1}}=\frac{-1}{3}\left[ \,\begin{matrix} -1 & -2 \\ -2 & -1 \\ \end{matrix}\, \right]\]\[=\frac{1}{3}\left[ \,\begin{matrix} 1 & 2 \\ 2 & 1 \\ \end{matrix}\, \right]\] and \[X={{A}^{-1}}B\] = \[\left[ \,\begin{matrix} \frac{1}{3} & \frac{2}{3} \\ \frac{2}{3} & \frac{1}{3} \\ \end{matrix}\, \right]\,\left[ \begin{align} & 3 \\ & 1 \\ \end{align} \right]\]; \[X=\frac{1}{3}\left[ \begin{align} & 5 \\ & 7 \\ \end{align} \right]\].You need to login to perform this action.
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