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Consider the matrix \(\mathbf{A} = \begin{pmatrix} 7 & -4 \\ 8 & -5 \end{pmatrix}\).
  1. Find the eigenvalues \(\lambda_1\) and \(\lambda_2\) of matrix \(\mathbf{A}\).
  2. Find the corresponding eigenvectors \(\mathbf{x}_1\) and \(\mathbf{x}_2\).

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