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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
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B
16
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C
31/2
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D
33/2
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Solution

The correct option is D $$33/2$$
Given system has a non-trivial solution.
$$\begin{vmatrix} 3 & k & -2 \\ 1 & k & 3 \\ 2 & 3 & -4 \end{vmatrix}=0$$

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

Hence, option D.

Mathematics

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