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

Question

Aicharya · Accepted Answer

$\left|\begin{array}{lll}4 & k & 2 \ k & 4 & 1 \ 2 & 2 & 1\end{array}ight|=0 \Rightarrow k^2-6 k+8=0 \Rightarrow k=4,2$

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…