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Q.

Let S denote the set of all real values of λ such that the system of equations λx+y+z=1,x+λy+z=1,x+y+λz=1 is inconsistent, then λS|λ|2+|λ| is equal to 

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a

2

b

12

c

6

d

4

answer is D.

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Detailed Solution

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λ111λ111λ=0λ33λ+2=0λ+2λ-12=0 λ=2,λ=1
If λ = 1 the system has infinitely many solutions
If λ = -2 the system is inconsistent
λS|λ|2+|λ|=4+2=6

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