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Question Number 205155 by depressiveshrek last updated on 10/Mar/24
Find the determinant:   determinant (((1−λ),1,1,…,1),(1,(1−λ),1,…,1),(1,1,(1−λ),…,1),(⋮,⋮,⋮,⋱,⋮),(1,1,1,…,(1−λ)))
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{determinant}: \\ $$$$\begin{vmatrix}{\mathrm{1}−\lambda}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}−\lambda}&{\mathrm{1}}&{\ldots}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}−\lambda}&{\ldots}&{\mathrm{1}}\\{\vdots}&{\vdots}&{\vdots}&{\ddots}&{\vdots}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\ldots}&{\mathrm{1}−\lambda}\end{vmatrix} \\ $$

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