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Consider the matrix \(\mathbf{A} = \begin{pmatrix} 3 & 2 \\ 2 & 0 \end{pmatrix}\).
One of the eigenvalues of this matrix is \(\lambda = 4\).
Find the eigenvector \(\mathbf{x} = \begin{pmatrix} x \\ y \end{pmatrix}\) corresponding to this eigenvalue.
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