Let \({A} = \begin{pmatrix} 0 & 5 & 7 \\ -2 & 7 & 7 \\ -1 & 1 & 4 \end{pmatrix}\). Find all values of \(t\) such that \(\det (t{I} - {A}) = 0\), where \(I\) is the \(3 \times 3\) identity matrix.
This is asking for the eigenvalues of matrix A:
+116 
