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Let S be the set of all $\lambda\in R$ 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

(1) is a singleton

(2) contains exactly two elements

(3) contains more than two elements

(4) is an empty set
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Ans. (2) contains exactly two elements

Sol. For no. solution Δ = 0 and at least one of Δ1, Δ2, Δ3 is non-zero.




Hence, $S=\{1,-{1\over2}\}$

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