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Let S be the set of all λ ∈ R for which the system of linear equations 2x - y + 2z = 2, x - 2y + λz = -4, x + λy + z = 4 has no solution. Then the set S
- contains more than two elements.
- is a singleton.
- contains exactly two elements.
- is an empty set.
Correct answer: contains exactly two elements.
Solution
The system of linear equations has no solution when the determinant of the coefficient matrix is zero, leading to a specific condition on λ that results in exactly two values where the system becomes inconsistent.
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