Let λ ∈ R . The system of linear equations 2 x 1 - 4 x 2 + λ x 3 = 1 x 1 - 6 x 2 + x 3 = 2 λ x 1 - 10 x 2 + 4 x 3 = 3 is inconsistent for :

Step-by-step solution

Here, we will use Cramer's Rule according to which, D = 0 and, D 1 ≠ 0 if the system of linear equations is inconsistent. D = 2 - 4 λ 1 - 6 1 λ - 10 4 = 2 - 24 + 10 + 4 4 - λ + λ - 10 + 6 λ = 2 3 λ 2 - 7 λ - 6 = 2 λ - 3 3 λ + 2 D = 0 ⇒ λ = 3 , - 2 3 D 1 = 1 - 4 λ 2 - 6 1 3 - 10 4 = 1 - 24 + 10 + 4 8 - 3 + λ - 20 + 18 = 2 3 - λ For    λ = - 2 3 , D 1 ≠ 0