A) 1
B) 0
C) 2
D) 3
Correct Answer: D
Solution :
Given system of equations is \[x+y+z=6\] \[x+2y+3z=10\] \[x+2y+\lambda z=0\]It has unique solution. \[\therefore \]\[\left| \begin{matrix} 1 & 1 &1 \\ 1 & 2 &3 \\ 1 & 2 & \lambda \\ \end{matrix} \right|\ne 0\] \[\Rightarrow \]\[1(2\lambda -6)-1(\lambda -3)+1(2-2)\ne 0\] \[\Rightarrow \]\[2\lambda -6-\lambda +3\ne 0\Rightarrow \lambda =3\ne 0\Rightarrow \lambda \ne 3\]
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