The system of linear equations 3 x - 2 y - k z = 10 2 x - 4 y - 2 z = 6 x + 2 y - z = 5 m is inconsistent if :

Step-by-step solution

For inconsistent system of equation the conditions should be ∆ = 0 and at least one of the ∆ x   or   ∆ y   or   ∆ z should not be equal to zero. Now, Δ = 3 - 2 - k 2 - 4 - 2 1 2 - 1 = 0 ⇒ 24 + 2 0 - k 8 = 0 ⇒ k = 3 And, Δ x = 10 - 2 - 3 6 - 4 - 2 5   m 2 - 1 ⇒ ∆ x = 10 8 - 2 - 10   m + 6 - 3 12 + 20   m ⇒ ∆ x = 8 4 - 5 m ∆ x ≠ 0 ⇒ m ≠ 4 5 Δ y = 3 10 - 3 2 6 - 2 1 5   m - 1 = 3