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The set of all values of λ for which the system of linear equations
x - 2y - 2z = λx
x + 2y + z = λy
-x - y = λz
has a non-trivial solutions:
- is an empty set
- contains more than two elements
- is a singleton
- contains exactly two elements
Correct answer: is a singleton
Solution
The system of equations can be rewritten in matrix form, and for non-trivial solutions to exist, the determinant of the coefficient matrix must be zero. Solving for λ reveals that there is only one specific value that satisfies this condition, indicating that the set of values for which non-trivial solutions exist is a singleton.
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