A) \[\lambda =1\]
B) \[\lambda =2\]
C) \[\lambda =-2\]
D) \[\lambda =3\]
Correct Answer: D
Solution :
Given system will be inconsistent when \[D=0\] \[\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 2 & \lambda \\ \end{matrix}\, \right|\,=0\] Applying \[{{C}_{1}}\to {{C}_{1}}-{{C}_{2}}\] and \[{{C}_{2}}\to {{C}_{2}}-{{C}_{3}}\] Þ \[\left| \,\begin{matrix} 0 & 0 & 1 \\ -1 & -1 & 3 \\ -1 & 2-\lambda & \lambda \\ \end{matrix}\, \right|\,=0\]Þ \[-1(2-\lambda )-1=0\Rightarrow \lambda =3\].
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