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# Given : $2x-y+2z=2,x-2y+z=-4,x+y+\lambda z=4$ then the value of $\lambda$ such that the given system of equation has No solution is

$(a)\;3\qquad(b)\;1\qquad(c)\;0\qquad(d)\;-3$

Since the system has no solution $\Delta =0$ and any one amongst $\Delta_x,\Delta _y,\Delta_z$ is non zero.
$\begin{vmatrix} 2&-1&2\\1&-2&1\\1&1&\lambda\end{vmatrix}=0$
$\Rightarrow \lambda=1$
$\Delta_z=\begin{vmatrix} 2&-1&2\\1&-2&-4\\1&1&1\end{vmatrix}=6\neq 0$
Hence (b) is the correct answer.