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Soit \(A=\left( \begin{array}{cccc} 0&\ldots&0&1\\ \vdots&\mathinner{\mkern 2mu\raise 1pt\hbox{.}\mkern 3mu\raise 4pt\hbox{.}\mkern 1mu\raise 7pt\hbox{{.}}}&\mathinner{\mkern 2mu\raise 1pt\hbox{.}\mkern 3mu\raise 4pt\hbox{.}\mkern 1mu\raise 7pt\hbox{{.}}}&0\\ 0& \mathinner{\mkern 2mu\raise 1pt\hbox{.}\mkern 3mu\raise 4pt\hbox{.}\mkern 1mu\raise 7pt\hbox{{.}}}& \mathinner{\mkern 2mu\raise 1pt\hbox{.}\mkern 3mu\raise 4pt\hbox{.}\mkern 1mu\raise 7pt\hbox{{.}}}&\vdots\\ 1&0&\ldots&0 \end{array} \right)\)
Montrer que \(A\) est diagonalisable.