(2−λ)x1−2x2+x3=0
2x1−(λ+3)x2+2x3=0
−x1+2x2−λx3=0
The systems of linear equations will have a non-trivial solution
⇒∣2−λ2−1−2−λ−3212−λ∣=0
⇒(2−λ)[λ2+3λ−4]+2[−2λ+2]+1[4−λ−3]=0
2λ2+6λ−8−λ3−3λ2+4λ−4λ+4+1−λ=0
−λ3−λ2+5λ−3=0
λ3+λ2−5λ+3=0
(λ−1)(λ2+2λ−3)=0
(λ−1)(λ+3)(λ−1)=0
⇒λ=−3,1,1