4. (Linear Algebra) If \( [A] = \begin{bmatrix} 3 & 0 & 0 \\ -3 & 4 & 9 \\ 0 & 0 & 3 \end{bmatrix} \), determine the eigenvalues of \( [A] \), find an eigenbasis of \( [A] \), and conduct diagonalization of \( [A] \). (25%)