A) \[-4-7i\]
B) \[4+7i\]
C) \[3+7i\]
D) \[7+4i\]
Correct Answer: B
Solution :
\[\Delta =(2+i)\,\left| \,\begin{matrix} 1 & 1 & i \\ 1 & 1+2i & 1+i \\ 1 & 2 & 1-i \\ \end{matrix}\, \right|\,\] =\[(2+i)\]\[\left| \,\begin{matrix} 0 & -2i & -1 \\ 0 & -1+2i & 2i \\ 1 & 2 & 1-i \\ \end{matrix}\, \right|\] by \[\begin{align} & {{R}_{1}}\to {{R}_{1}}-{{R}_{2}} \\ & {{R}_{2}}\to {{R}_{2}}-{{R}_{3}} \\ \end{align}\] = \[(2+i)\,\,\{-4{{i}^{2}}+(-1+2i)\}=(2+i)\,(4-1+2i)\] = \[(2+i)\,(3+2i)=4+7i\].
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