Question:
Let $\lambda$ be a real number for which the system of linear equations
$x+y+z=6$
$4 x+\lambda y-\lambda z=\lambda-2$
$3 x+2 y-4 z=-5$
has infinitely many solutions. Then $\lambda$ is a root of the quadratic equation.
Correct Option: , 2
Solution:
$\mathrm{D}=0$
$\left|\begin{array}{ccc}1 & 1 & 1 \\ 4 & \lambda & -\lambda \\ 3 & 2 & -4\end{array}\right|=0 \Rightarrow \lambda=3$
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