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Q.
Given : $2 x - y -4 z =2, x -2 y - z =-4, x + y +\lambda z =4$, then the value of $\lambda$ such that the given system of equation has NO solution, is
Determinants
Solution:
Since the system has no solution
$\begin{vmatrix}2 & -1 & -4 \\ 1 & -2 & -1 \\ 1 & 1 & \lambda\end{vmatrix}=0 $
$\Rightarrow 2(-2 \lambda+1)+1(\lambda+1)-4(3)=0$
$\Rightarrow -4 \lambda+2+\lambda+1-12=0$
$ \Rightarrow -3 \lambda=9 $
$\Rightarrow \lambda=-3$