= Solution
The <Jacobian matrix> at the extinction <fixed point> is
$$
J_0=\begin{pmatrix}0&r/b^2\\c&1-d\end{pmatrix},
$$
with <characteristic polynomial>
$$
p(q)=q^2-(1-d)q-\frac{cr}{b^2}.
$$
Under $cr>db^2$, $p(1)=d-cr/b^2<0$, whereas $p(q)\to\infty$ as $q\to\infty$. Hence its positive <eigenvalue>
$$
q_+=\frac{1-d+\sqrt{(1-d)^2+4cr/b^2}}2
$$
is greater than one. Its <eigenvector> can be taken with both components positive: choose $(r/(b^2q_+),1)^T$. Thus there are biologically admissible positive perturbations that grow. \b[The extinction <fixed point> is unstable] by <linear stability analysis> for a <discrete dynamical system>.
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