Question

Compute the determinant of the \(n \times n\) matrix whose elements are identified by the condition \(a_{ij} = \min(i,j)\), where \(i\) is the row number and \(j\) is the column number.

• A. -1
• B. \( (-1)^n \)
• C. 1
• D. 0

Hint:

For matrices with elements defined as the minimum of row and column indices, the determinant is always 1.

Answer 1

The Correct Option is C

The matrix is a special matrix known as a "min matrix," where each element is the minimum of its row and column indices. It is known that the determinant of such a matrix, regardless of the size, equals 1. This is a result derived from properties of the Vandermonde-like matrices.