Answer: (b-a)(c-a)(c-b).
- A (b-a)(c-a)(c-b)
- B a2+b2+c2-ab-bc-ca
- C (a+b+c)3
- D abc(a+b+c)
Correct answer: A. (b-a)(c-a)(c-b)
Explanation: Vandermonde matrix V = [[1,1,1],[a,b,c],[a²,b²,c²]]. Apply column ops: C2−C1, C3−C1, then factor - det = (b−a)(c−a)(c−b). Non-zero iff all values are distinct. Answer: (b−a)(c−a)(c−b).
Element aij of matrix A sits at the intersection of row i and column j.
Concept context
Matrix operations, determinants, inverses, and solving linear systems