Question

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 

(1) contains more than two elements. 

(2) is a singleton. 

(3) contains exactly two elements.

(4) is an empty set.

Answer 1

Answer is (3) contains exactly two elements.

2x – y + 2z = 2

x–2y + λz = –4

x + λy + z = 4

For no solution :

= 2(1 + λ)

which is not equal to zero for

λ = 1, \(-\frac{1}{2}\)