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  4. Given, 2x - y + 2z = 2, x - 2y + z = -4 , x + y + λ z = 4, then the value of λ such th a t the given system of equations has no solution, is

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Q. Given, $2x - y + 2z = 2, x - 2y + z = -4 , x + y + \lambda z = 4$, then the value of $\lambda$ such th a t the given system of equations has no solution, is

IIT JEEIIT JEE 2004Determinants

Solution:

Since, given system has no solution.
$\therefore \Delta= 0 $ and any one amongst $\Delta_x,\Delta_y,\Delta_z$ is non-zero .
Let $\therefore \begin {vmatrix}2 & -1 & 2 \\1 & -2 & 1 \\1 & 1 & \lambda \end {vmatrix} =0 $ and $ \Delta_z= \begin {vmatrix}2 & -1 & 2 \\1 & -2 & -4 \\1 & 1 & 4 \end {vmatrix} =6 \ne 0$
$\Rightarrow \lambda=1$