Question

The value of k for which the set of equations $3x+ky-2z=0,x+ky+3z=0$ and $2x+3y-4z=0$ has a non-trivial solution is-

• A. $15$
• B. $16$
• C. $31/2$
• D. $33/2$

Answer 1

The correct option is D $33/2$

Given system has a non-trivial solution.
$\left|\begin{array}{ccc}3& k& -2\\ 1& k& 3\\ 2& 3& -4\end{array}\right|=0$

$\Rightarrow 3(-4k-9)+10k-2(3-2k)=0$
$\Rightarrow 2k=33$
$\therefore k=33/2$

Hence, option D.