Find the real values of `lambda` for which the following system of linear equations has non-trivial solutions. `2lambdax-2y+3z=0` `x+lambday+2z=0` `2x+lambdaz=0`

Explanation

To find the real values of \( \lambda \) for which the following system of linear equations has non-trivial solutions, we need to analyze the determinant of the coefficient matrix formed by the equations. The equations are:

1. \( 2\lambda x - 2y + 3z = 0 \)
2. \( x + \lambda y + 2z = 0 \)
3. \( 2x + \lambda z = 0 \)

### Step 1: Form the Coefficient Matrix
The coefficient matrix \( A \) for the system of equations can be represented as follows:
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