# 2015-18 Determinant

What is the determinant of the $$n\times n$$ matrix $$A_n=(a_{ij})$$ where $a_{ij}=\begin{cases} 1 ,&\text{if } i=j, \\ x, &\text{if }|i-j|=1, \\ 0, &\text{otherwise,}\end{cases}$ for a real number $$x$$?

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