A) \[\left[ \begin{matrix} 1 & 1 \\ 2 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2/3 & 1/3 \\ 1/3 & 2/3 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 1/3 & 1/3 \\ 2/3 & 1/3 \\ \end{matrix} \right]\]
D) None of these
Correct Answer: C
Solution :
\[2A+2B=\left[ \begin{matrix} 2 & 0 \\ 2 & 2 \\ \end{matrix} \right]\], \[A-2B=\left[ \begin{matrix} -1 & 1 \\ 0 & -1 \\ \end{matrix} \right]\] On adding, we get\[3A=\left[ \begin{matrix} 1 & 1 \\ 2 & 1 \\ \end{matrix} \right]\] \[\Rightarrow \,A=\left[ \begin{matrix} 1/3 & 1/3 \\ 2/3 & 1/3 \\ \end{matrix} \right]\].
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