Question

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

Answer 1

Given system of equations

$3x-2y+z=0$

$\lambda x-14y+15z=0$

$x+2y-3z=0$ have non-zero solution

$\left|\begin{array}{ccc}3& -2& 1\\ \lambda & -14& 15\\ 1& 2& -3\end{array}\right|=0$

$\Rightarrow 3(42-30)+2(-3\lambda -15)+1(2\lambda +14)=0$

$\Rightarrow 36-6\lambda -30+2\lambda +14=0$

$\Rightarrow -4\lambda =-20$

$\therefore \lambda =5$