Matrix/Nilpotent/Jordan/Successive kernels/1/Exercise

Determine the kernels of the powers ${}M^{i}$ of the matrix

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

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