The value of λfor which the system of equations x−2y−2z=λx,x+2y+z=λy,−x−y−λz=0 has a non-trivial solution is

The system has a non – trivial solution⇒Δ=0 ⇒1−λ−2−212−λ1−1−1−λ=0    apply R1→ R1+ R3, R2→ R2+ R3 ⇒−λ−3−2-λ01−λ1−λ−1−1−λ=0 ⇒λ−3−2-λ01−λ1−λ1−1−λ=0 ⇒λ−λ1−λ+11−λ-0+1-31−λ+1−λ2+λ=0 ⇒λλ-12-λ-12=0 ⇒λ-13=0 ⇒λ=1  ⇒λ=1