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matrix determinant problem

Source: Romanian District Olympiad 2000, Grade XI, Problem 2

September 24, 2018
linear algebramatrixdeterminant

Problem Statement

Calculate the determinant of the n×n n\times n complex matrix (aji)1≤j≤n1≤i≤n \left(a_j^i\right)_{1\le j\le n}^{1\le i\le n} defined by aji={1+x2,emsp;i=jx,emsp;∣i−j∣=10,emsp;∣i−j∣≥2, a_j^i=\left\{\begin{matrix} 1+x^2,  i=j\\x,  |i-j|=1\\0,  |i-j|\ge 2\end{matrix}\right. , where n n is a natural number greater than 2. 2.
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