Jordan-Block/2/Potenzen/Induktion/Aufgabe

Es sei

{}M={\begin{pmatrix}\lambda &1\\0&\lambda \end{pmatrix}}\,

mit ${}\lambda \in K$ . Zeige durch Induktion, dass

{}M^{n}={\begin{pmatrix}\lambda ^{n}&n\lambda ^{n-1}\\0&\lambda ^{n}\end{pmatrix}}\,

ist.

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