(b) Determine the kernel of L

6. (20%) Let the matrix $\mathbf{A} = \begin{bmatrix} 3 & -1 & -2 \\ 2 & 0 & -2 \\ 2 & -1 & -1 \end{bmatrix}$. Answer the following questions: (a) Find the eigenvalues and eigenvectors of the matrix $\mathbf{A}$.

(b) Determine the kernel of \(L\)

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