Answer: (b-a)(c-a)(c-b).
- A (b-a)(c-a)(c-b)
- B a<sup>2</sup>+b<sup>2</sup>+c<sup>2</sup>-ab-bc-ca
- C (a+b+c)<sup>3</sup>
- 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: C<sub>2</sub>−C<sub>1</sub>, C<sub>3</sub>−C<sub>1</sub>, 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