Find the value of `lambda` for which the homogeneous system of equations: `2x+3y-2z=0` `2x-y+3z=0` `7x+lambday-z=0` has non-trivial solutions. Find the solution.

Explanation

To find the value of \( \lambda \) for which the homogeneous system of equations has non-trivial solutions, we need to set up the system in matrix form and calculate the determinant. The system of equations is:

1. \( 2x + 3y - 2z = 0 \)
2. \( 2x - y + 3z = 0 \)
3. \( 7x + \lambda y - z = 0 \)

We can represent this system in matrix form as follows:

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