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A class of matrices with zero determinant. (English)
Math. Mag. 85, No. 2, 126-130 (2012).
Summary: Let $a_{1}, a_{2},\dots, a_{n}, b_{1}, b_{2},\dots, b_{n}$ be real numbers and the $n \times n$ matrix $C$ be defined with entries $c_{ij} =(a_{i} + b_{j})^{k}$, where $k$ is a positive integer. If $n > k + 1$, then $\det(C) =0$, and if $n = k + 1$, then $\det(C)$ is a product involving two Vandermonde determinants.
Classification: H60