Question

The value of $\lambda$, such that the following system of equations has no solution, is
$\begin{array}{c}2x-y-2z=2\\ x-2y+z=-4\\ x+y+\lambda z=4\end{array}$

• A. $3$
• B. $1$
• C. $0$ (Zero)
• D. $-3$

Answer 1

The correct option is D $-3$

$\Delta$ must be $0$, for the system of equations to have no solution.
$\Rightarrow \left|\begin{array}{ccc}2& -1& -2\\ 1& -2& 1\\ 1& 1& \lambda \end{array}\right|=0\Rightarrow 2(-2\lambda -1)+1(\lambda -1)-2(1+2)=0\Rightarrow -3\lambda -9=0\Rightarrow \lambda =-3$