If the system of equations λx1+x2+x3=1, x1+λx2+x3=1,  x1+x2+λx3=1 is inconsistent, then λ= ___________

The necessary condtion for a non-homogeneous system of equations to be inconsistent is Δ=0 ⇒λ111λ111λ=0      C1→C1+C2+C2   =λ+211λ+2λ1λ+21λ    =λ+21    1     11    λ    11      1    λ          R1→R1−R2:, R2→R2−R3      =λ+20   1−λ   00    λ−1  1−λ1        1                  λ       =λ+20λλ-1-1-λ−1−λ0−1−λ=λ+21−λ2=0⇒λ=−2,1