Question
Mathematics Question on Determinants
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 λ∈S∑(∣λ∣2+∣λ∣) is equal to
A
12
B
4
C
2
D
6
Answer
6
Explanation
Solution
The correct answer is (D) : 6
λ 1 11λ111λ=0
(λ+2)λ 1 11λ111λ=0
(λ+2)[1(λ2−1)−1(λ−1)+(1−λ)]=0
(λ+2)[(λ2−2λ+1)=0
(λ+2)(λ−1)2=0⇒λ=−2,λ=1
at λ=1 system has infinite solution, for inconsistent λ=−2
so ∑(∣−2∣2+∣−2∣)=6