Given 2 x-y+2 z=2, x-2 y+z=-4 , x+y+λ z=4 , then the value of λ...

Since, the system has no solution. \left|$$\begin{array}{ccc}2 & -1 & 2 \\ 1 & -2 & -1 \\ 1 & 1 & \lambda\end{array}$$\right|=0\Rightarrow 2(-2 \lambda+1)+1(\lambda+1)+2(3)=0\Rightarrow \quad-4 \lambda+2+\lambda+1+6=0\Rightarrow \quad 3 \lambda=9 \Rightarrow \lambda=3