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 determinant of the coefficients of the equations and solve for \( \lambda \).

### Step 1: Write the system of equations in matrix form

The given equations are:
1. \( 2x + 3y - 2z = 0 \)
2. \( 2x - y + 3z = 0 \)
3. \( 7x + \lambda y - z = 0 \)
...