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The set of all values of λ for which the system of linear equations:
2x − 2x + z = λx,
2x1 − 3x2 + 2x3 = λx2,
−x1 + 2x2 = λx3
has a non-trivial solution,
- contains two elements.
- contains more than two elements
- is an empty set.
- is a singleton
Correct answer: contains two elements.
Solution
The characteristic equation factors as (lambda-1)^2(lambda+3)=0, giving lambda=1 and lambda=-3, so the set has exactly two elements.
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