Find the eigenvalues of the matrix \begin{equation*} A = \begin{bmatrix} -7 & 0 & 0 \ -2 & 1 & 0 \ 3 & -1 & 0 \end{bmatrix}. \end{equation*} Also, write the characteristic polynomial of the matrix $A$ in the form of $a\lambda^3 + b\lambda^2 + c\lambda + d$.
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