If the system of equations
Question:

If the system of equations $2 x+3 y-z=0, x+$ $\mathrm{ky}-2 \mathrm{z}=0$ and $2 \mathrm{x}-\mathrm{y}+\mathrm{z}=0$ has a non-trival

solution $(\mathrm{x}, \mathrm{y}, \mathrm{z})$, then $\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{z}}+\frac{\mathrm{z}}{\mathrm{x}}+\mathrm{k}$ is equal to:-

 

  1. $\frac{3}{4}$

  2. $-4$

  3. $\frac{1}{2}$

  4. $-\frac{1}{4}$


Correct Option: , 3

Solution:

 

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