Given 2x−y+2z=2, x−2y+z=−4, x+y+λz=4, then the value of λ such that the given system of equations has no solution is

The condition for a non-homogeneous system to have a no solution is rankA≠rankAD Now, augmented matrix AD=2-1221-21-411λ4                                                           R2→2R2-R1, R3→2R3-R1                                                      ~2-1220-30-10032λ-26                                                          R3→R3+R2                                                      ~2-1220-30-10002λ-2-4 If 2λ-2=0, then rankA=2,rankAD=3 so that rankA≠rankAD. ∴2λ-2=0⇒λ=1