Question

The system of equations
$2x-y+z=0$
$x-2y+z=0$
$\lambda x-y+2z=0$
has infinite number of non-trivial solutions for

• A. $\lambda =1$
• B. $\lambda =3$
• C. $\lambda =-5$
• D. non real value of $\lambda$

Answer 1

The correct option is B $\lambda =3$

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

$\Rightarrow 2(-4+1)+1(\lambda -2)+1(-1+2\lambda )=0$

$\Rightarrow -6+\lambda -2-1+2\lambda =0$

$\Rightarrow \lambda =3$

Hence, option 'B' is correct.