Question

The system of equations 3x-2y $+z=0,\lambda x-14y+15z=0$ and $x+2y-3z=0$ have non-zero solution, then $\lambda =$

• A. $1$
• B. $3$
• C. $5$
• D. $0$

Answer 1

Answer: (C)

$5$

$\Delta =\left|\begin{array}{ccc}3& -2& 1\\ \lambda & -14& 15\\ 1& 2& -3\end{array}\right|$
Now $\Delta =0$ for non-zero solution
$\therefore \Delta =36-6\lambda -30+2\lambda +14$
$\Delta =20-4\lambda =0$
$\therefore \lambda =5$