Question

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

• A. 3
• B. 1
• C. 0
• D. -3

Answer 1

Answer: (D)

Since the system has no solution
$\left|\begin{array}{ccc}2& -1& -4\\ 1& -2& -1\\ 1& 1& \lambda \end{array}\right|=0$
$\Rightarrow 2(-2\lambda +1)+1(\lambda +1)-4(3)=0$
$\Rightarrow -4\lambda +2+\lambda +1-12=0$
$\Rightarrow -3\lambda =9$
$\Rightarrow \lambda =-3$