The system of equations - k x + 3 y - 14 z = 25 - 15 x + 4 y - k z = 3 - 4 x + y + 3 z = 4 Question: is consistent for all k in the set

Step-by-step solution

For consistent solutions ∆ ≠ 0 ⇒ - k 3 - 14 - 15 4 - k - 4 1 3 ≠ 0 ⇒     - k 12 + k - 3 - 45 - 4 k - 14 - 15 + 16 ≠ 0 ⇒   - 12 k - k 2 + 135 + 12 k - 14 ≠ 0 ⇒   k 2 ≠ 121 ⇒   k ≠ 11 , - 11