A) \[\left[ \begin{matrix} 1/2 & 2 \\ 1/2 & 1 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 2 & 2 \\ 1/2 & 1/2 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 1/2 & -2 \\ -1/2 & 1 \\ \end{matrix} \right]\]
D) None of these
Correct Answer: C
Solution :
\[{{A}_{2\times 2}}=[{{a}_{ij}}]=\left[ \begin{matrix} {{a}_{11}} & {{a}_{12}} \\ {{a}_{21}} & {{a}_{22}} \\ \end{matrix} \right]\] \[{{a}_{ij}}=\frac{1}{2}|2i-3j|\] \[\therefore \] \[{{a}_{11}}=\frac{1}{2}|2-3|=\frac{1}{2}\] \[{{a}_{12}}=\frac{1}{2}|2-6|=2\] \[{{a}_{21}}=-\frac{1}{2}|4-3|=\frac{1}{2}\] \[{{a}_{22}}=\frac{1}{2}|4-6|=1\] \[{{A}_{2\times 2}}=\left[ \begin{matrix} \frac{1}{2} & 2 \\ \frac{1}{2} & 1 \\ \end{matrix} \right]\]
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