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Question

The sum of distinct values of λ for which the systems of equations
(λ1)x+(3λ+1)y+2λz=0
(λ1)x+(4λ2)y+(λ+3)z=0
2x+(3λ+1)y+3(λ1)z=0
has non-zero solutions, is


A
3.000
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B
3
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C
3.0
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D
3.00
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Solution

∣ ∣λ13λ+12λλ14λ2λ+323λ+13(λ1)∣ ∣=0
R2R2R1
R3R3R1
∣ ∣λ13λ+12λ0λ3λ+33λ0λ3∣ ∣=0
C1C1+C3
∣ ∣3λ13λ+12λλ+3λ3λ+300λ3∣ ∣=0
(λ3)[(3λ1)(λ3)(3λ)(3λ+1)]=0
(λ3)[3λ210λ+3(8λ3λ2+3)]=0
(λ3)(6λ218λ)=0
(6λ)(λ3)2=0
λ=0,3
sum of values of λ=0+3=3



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