Find the eigenvalues, eigenvectors, AM, and GM of each eigenvalue and decide whether the matrix is defective

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Find the eigenvalues, eigenvectors, AM, and GM of each eigenvalue and decide whether the matrix is defective or not. Then, transform the matrix into either a diagonal or a Jordan matrix, whichever is applicable.

\(\mathbf{A}=\left[\begin{array}{lll}2 & 2 & 1 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]\)

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