Question

$\text{The value of}\lambda \text{such that the system given below does not have any solution is \_\_\_\_\_\_.}$
$x-2y+z=-4$
$2x-y+2z=2$
$x+y+\lambda z=4$

• A. 1

Answer 1

The correct option is A 1
For no solution $D=0$
$\left|\begin{array}{ccc}1& -2& 1\\ 2& -1& 2\\ 1& 1& \lambda \end{array}\right|=0$
$(-\lambda -2)+2(2\lambda -2)+\left(3\right)=0$
$\Rightarrow -\lambda -2+4\lambda -4+3=0$
$\Rightarrow 3\lambda -3=0$
$\Rightarrow \lambda =1$