If the values of λfor which the system of linear equations 2x1−2x2+x3=λx1, 2x1−3x2+2x3=λx2 ,−x1+2x2=λx3 has non – trivial solution are λ1,λ2,λ3then λ12+λ22+λ32/1000=

The system has a non – trivial solution⇒Δ=0 ⇒2−λ−212−3−λ2−12−λ=0 ⇒2−λλ3+λ-4+2-2λ+2+14-3+λ=0 ⇒2−λλ2+3λ-4-4λ+4+1-λ=0 ⇒2λ2+6λ-8-λ3-3λ2+4λ-5λ+5=0 ⇒λ3+λ2-5λ+3=0 ⇒λ-1λ2+2λ-3=0 ⇒λ-1λ-1λ+3=0 ⇒λ=1,1,-3=λ1, λ2,λ3say ∴λ12+λ22+ λ321000=1+1+91000=111000=0.011