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Let A=\left[\begin{array}{ccc}

-3 & 2 & 6 \\

0 & -1 & 0 \\

-1 & 1 & 2

\end{array}\right] ) Find the characteristic polynomial and the eigenvalues of A. ) Find a basis for each eigenspace of A. (c) (3 marks) If A is diagonalizable, explain why and then diagonalize A, that is, find an invertible matrix P and a diagonal matrix D such that P-1 AP = D. If A is not diagonalizable, then explain why it is not diagonalizable.

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