Problem 770 (difficulty: 9/10)

Let \(\displaystyle a_1<a_2<\ldots<a_n\) and \(\displaystyle b_1<b_2<\ldots<b_n\) be real numbers Show that

\(\displaystyle \det\begin{pmatrix} e^{a_1b_1} & e^{a_1b_2} & \dots & e^{a_1b_n} \\ e^{a_2b_1} & e^{a_2b_2} & \dots & e^{a_2b_n} \\ \vdots & \vdots & \ddots & \vdots \\ e^{a_nb_1} & e^{a_nb_2} & \dots & e^{a_nb_n} \\ \end{pmatrix} >0. \)

(KöMaL A. 463., October 2008)

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