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**Let [tex]A[/tex] be a matrix and [tex]\mu[/tex] be an eigenvalue of that matrix. Suppose that for some [tex]k[/tex], [tex]\tex{ker}\left(A-\mu I\right)^k=\tex{ker}\left(A-\mu I\right)^{k+1}[/tex]. Then show that [tex]\tex{ker}\left(A-\mu I\right)^{k+r}=\tex{ker}\left(A-\mu I\right)^{k+r+1}[/tex] for all [tex]r\geq0[/tex]**.