Let \(\mathbf{A} = \begin{pmatrix} 0 & 5 & 7 \\ -2 & 7 & 7 \\ -1 & 1 & 4 \end{pmatrix}\) Find all values of \(l\) such that \(\det (t \mathbf{I} - \mathbf{A}) = 0\), where \(\mathbf{I}\) is the \(3 \times 3\) identity matrix.
The possible values of t are -1, 2, and 5.
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