The value of \(k\) for which the set of equations \(3 x+k y-2 z=0, x+k y+3 z=0\) and \(2 x+3 y-4 z=0\) has a non-trivial solution, is
To get non trivial solutions, \[\] \(\left|\begin{array}{ccc}3 & k & -2 \\ 1 & k & 3 \\ 2 & 3 & -4\end{array}\right|=0\) \[\] \(\Rightarrow 3(-4 k-9)-k(-4-6)-2(3-2 k=0)\) \[\] \(\Rightarrow 2 k-33=0\) or \(k=\frac{33}{2}\). \[\] Choice (D)\[\]
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