4. If \( A] = \begin{bmatrix} 3 & 0 & 0 \\ -3 & 4 & 9 \\ 0 & 0 & 3 \end{bmatrix} \), determine the eigenvalues of [A], find an eigenbasis 0 0 3 of [A], and conduct diagonalization of [A].
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4. If \( A] = \begin{bmatrix} 3 & 0 & 0 \\ -3 & 4 & 9 \\ 0 & 0 & 3 \end{bmatrix} \), determine the eigenvalues of [A], find an eigenbasis 0 0 3 of [A], and conduct diagonalization of [A].