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The values of k for which the system of equations $\begin{matrix} x + k y - 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0 \end{matrix}$ has a non-trivial solution is (are)

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Correct option is A

From (1) and (2), 2x+z=0⇒2x=-zFrom (3), we get 3y =5z∴x=-12z,y=53zSubstituting this in (1) we get -12z+5k3z-3z=0.⇒5k3-72z=0Now , z≠0⇒k=2110

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The values of k for which the system of equationsx+ky-3z=0 , 3x+ky-2z=0 , 2x+3y-4z=0 has a non-trivial solution is (are)

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The values of k for which the system of equations $\begin{matrix} x + k y - 3 z = 0, 3 x + k y - 2 z = 0, 2 x + 3 y - 4 z = 0 \end{matrix}$ has a non-trivial solution is (are)