I am stuck with the following problem:
Let $Y(x)=(y_{1}(x),y_{2}(x))$ and let $A$ is given by $\begin{pmatrix} -3 &1 \\ k& -1 \end{pmatrix}.$ Further, let $S$ be the set of values of $k$ for which all the solutions of the system of equations $Y'(x)=AY(x)$ tend to $0$ as $x$ tends to $\infty.$ Then $S$ is given by:
(a) $\{k:k\leq -1\}$
(b) $\{k:k\leq 3\}$
(c) $\{k:k<3\}$
(d) $\{k:k<-1\}.$
Please help. Thanks in advance for your time.