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The number of values of $\mathrm{k}$ for which the linear equations $4 x+k y+2 z=0 ; k x+4 y+z=0 ; 2 x+2 y+z=0$ possess a non-zero solution is
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$\left|\begin{array}{lll}4 & k & 2 \\ k & 4 & 1 \\ 2 & 2 & 1\end{array}\right|=0 \Rightarrow k^2-6 k+8=0 \Rightarrow k=4,2$
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