Let D<sub>k</sub> = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="|
Step-by-Step Solution
Key Concept: Evaluate the determinant D_k by performing row operations to simplify it, then sum the resulting expression from k=1 to n and equate to 96 to solve for n.
Performing R2 -> R2 - nR1 and R3 -> R3 - nR1 simplifies the determinant. After simplification, D_k becomes a linear function of k. Summing this from k=1 to n gives a quadratic in n, which is set to 96 to find n.
Correct Answer: 4