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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,

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

Correct answer: contains more than two elements

Solution

The system of equations can be analyzed using the determinant of the coefficient matrix. For a non-trivial solution to exist, the determinant must equal zero, which leads to a polynomial equation in λ that can have infinitely many solutions, indicating that the set of values for λ contains more than two elements.

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