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Consider the matrix \(\mathbf{C} = \begin{pmatrix} 2 & -1 \\ 3 & -2 \end{pmatrix}\) and the vector \(\mathbf{v} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}\).
  1. Calculate the product \(\mathbf{C}\mathbf{v}\).
  2. Hence, determine the eigenvalue \(\lambda\) associated with the eigenvector \(\mathbf{v}\).

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