The values of λ and μ for which the system of linear equations x + y + z = 2 , x + 2 y + 3 z = 5 , x + 3 y + λ z = μ has infinitely many solutions, are respectively

Step-by-step solution

For infinite number of solutions, all determinants D ,   D 1 ,   D 2   and   D 3 must be zero and planes represented by these equations should not be parallel. So, we have, D = 1 1 1 1 2 3 1 3 λ = 0   ⇒ λ = 5 D 1 = 2 1 1 5 2 3 μ 3 λ = 0 D 2 = 1 2 1 1 5 3 1 μ λ = 0 And D 3 = 1 1 2 1 2 5 1 3 μ = 0   ⇒ μ = 8