If the system of equations,λx+2y−2z=1, 4x+2λy−z=2,   6x+6y+λz=3  has a unique solution, then

The given system of equations can be written in a single matrix equation: [λ2−242λ−166λ][xyz]=[123] The given system of equations will have a unique solution if and only if the coefficient matrix is non-singular  i.e. iff|λ2−242λ−166λ|≠0 ∴   λ(2λ2+6)−2(4λ+6)−2(24−12λ)≠0 or   λ3+11λ−30≠0 or  (λ−2)(λ2+2λ+15)≠0   or  λ≠2  (only  real   root)