Step-by-Step Solution
Key Concept: Systematic row and column operations combined with factoring allows computation of the determinant expression.
Through the row operations shown: $R_1 \to R_1 - \lambda, R_2 \to R_2 - \mu, R_3 \to R_3 - \nu$ where $\lambda, \mu, \nu$ are chosen appropriately, the determinant is factored. After factoring out common terms from rows and columns, we obtain $K = 4\Delta^3 = 4 \times 1 = 4$.
Correct Answer: 4