Question

The system of equation $2x-y+2z=2$ $x-2y-z=-4,x+y+\lambda z=4$ has no solutions, then $\lambda$ is

• A. $-3$
• B. $1$
• C. $0$
• D. $3$

Answer 1

Answer: (D)

$3$

For no solution $\Delta =0$

$\left|\begin{array}{ccc}2& -1& 2\\ 1& -2& -1\\ 1& 1& \lambda \end{array}\right|=0$

or $2(-2\lambda +1)+1(\lambda +1)+2(1+2)=0$

$-4\lambda +2+\lambda +1+2+4=0$

$-3\lambda =-9$

$\therefore \lambda =3$