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Question

The set of all values of λ for which the system of linear equation :
2x12x2+x3=λx1,2x13x2+2x3=λx2x1+2x2=λx3 has a non-trivial solution

A
contains two elements
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B
contains more than two elements
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C
is an empty set
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D
is a singleton
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Solution

The correct option is A contains two elements
(2λ)x12x2+x3=0

2x1(3+λ)x2+2x3=0

x1+2x2λx3=0

Non-Trivial solution =0

∣ ∣2λ2123λ212λ∣ ∣=0

(2λ){3λ+λ24}+2[2λ+2}+(43λ)=0

(6λ+2λ283λ2λ3+4λ)4λ+4+1λ=0

λ3λ25λ+3=0

x3λ2+2λ22λ3λ+3=0

λ2(λ1)+2λ(λ1)3(λ1)=0

(λ1)=(λ2+2λ3)=0

(λ1)(λ+3)(λ1)=0

λ=1,1,3

Therefore, thus are only Two elements.

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