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The Vandermonde determinant for distinct values (a, b, c) equals:

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).

Matrix A (3 rows x 3 columns)a11a12a13a21a22a23a31a32a33column 1column 2column 3row 1row 2row 3

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

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