A) a singleton
B) an empty set
C) an infinite set
D) a finite set containing two or more elements
Correct Answer: A
Solution :
\[D=\left| \begin{matrix} 1 & 1 & 1 \\ 1 & a & 1 \\ a & b & 1 \\ \end{matrix} \right|=0\Rightarrow a=1\] and at \[a=1\] \[{{D}_{1}}={{D}_{2}}={{D}_{3}}=0\] \[\begin{matrix} \text{First}\,\text{two}\,\text{equations}\,\text{are} \\ \text{and}\,\text{third}\,\text{equation}\,\text{is} \\ \end{matrix}\left. \begin{matrix} x+y+z=1 \\ x+y+z=0 \\ \end{matrix} \right]\Rightarrow \text{There}\,\text{is}\,\text{no}\,\text{solution}\] \[\therefore \] \[b=\{1\}\Rightarrow \]it is a singleton set
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