The set of all values of `lambda` for which the systme of linear equations x-2y-2z =`lambda x, x +2y +z = lambda y " and "-x-y = lambdaz` has a non-trivial solution.

Options

A. contains exactly two elements
B. contains more than two elements
C. is a singleton
D. is an empty set

Explanation

To find the set of all values of \( \lambda \) for which the system of linear equations has a non-trivial solution, we start with the given equations:

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

### Step 1: Rearranging the equations
We can rearrange each equation to bring all terms to one side:
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