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For the system of linear equations 2x1 − 2x2 + x3 = λx1, 2x1 − 3x2 + 2x3 = λx2, −x1 + 2x2 = λx3, the set of all values of λ for which the system has a non-trivial solution:

1. contains two elements
2. contains more than two elements
3. is an empty set
4. is a singleton

Correct answer: contains two elements

Solution

The eigenvalue (characteristic) equation factors to give repeated/distinct roots whose distinct values number two, so the set of valid λ contains two elements.

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