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

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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