Question

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

• A. 3
• B. 1
• C. 0
• D. -3

Answer 1

Answer: (B)

Since, given system has no solution.
$\therefore \Delta =0$ and any one amongst ${\Delta }_x,{\Delta }_y,{\Delta }_z$ is non-zero .
Let $\therefore \left|\begin{array}{ccc}2& -1& 2\\ 1& -2& 1\\ 1& 1& \lambda \end{array}\right|=0$ and ${\Delta }_z=\left|\begin{array}{ccc}2& -1& 2\\ 1& -2& -4\\ 1& 1& 4\end{array}\right|=6\ne 0$
$\Rightarrow \lambda =1$