Question

The value of $\lambda$ such that the system of equations
$2x-y-2z=2;x-2y+z=-4;x+y+\lambda z=4$ has no solution, is

• A. $3$
• B. $1$
• C. $0$
• D. $-3$

Answer 1

Answer: (D)

$-3$

If the given system of equation has no solution,
then $\left|\begin{array}{ccc}2& -1& -2\\ 1& -2& 1\\ 1& 1& \lambda \end{array}\right|=0$
$\Rightarrow 2(-2\lambda -1)+1(\lambda -1)-2(1+2)=0$
$\Rightarrow -4\lambda -2+\lambda -1-6=0$
$\Rightarrow -3\lambda -9=0$
$\lambda =-3$