If the system of equations x+2y+3z=λx, 3x+y+2z=λy, 2x+3y+z=λz has non-trivial solution , then λ=……..
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Given system of equations ,
1−λx+2y+3z=0,3x+1−λ+2z=0, 2x+3y+1−λz=0
Has nontrivial solution ⇒1−λ2331−λ2231−λ=0
R1+R2+R3⇒6−λ6−λ6−λ31−λ2231−λ(6−λ)11131−λ2231−λC2−C1C3−C1
⇒(6−λ)1003−λ−2−121−λ−1=0⇒(6−λ)[(λ+1)(λ+2)+1]=0⇒λ=6,λ2+3λ+3=0