The number of values of k for which the linear equations `4x""+""k y""+""2z""=""0` `k x""+""4y""+""z""=""0` `2x""+""2y""+""z""=""0` posses a non-zero solution is : (1) 3 (2) 2 (3) 1 (4) zero

Explanation

To determine the number of values of \( k \) for which the given linear equations possess a non-zero solution, we will analyze the system of equations using the concept of determinants.

### Step-by-Step Solution:

1. **Write the System of Equations**:
The given equations are:
\[
4x + ky + 2z = 0 \quad \text{(1)}
...