MATLAB On a certain island, there is a population of snakes, foxes, hawks and mice. Their populations at time t are given by s(t), f(t), h(t), and m(t) respectively. The populations grow at rates given by the differential equations

,-41 16 16 m, 45 Putting the four populations into a vector y() = [s() f(t) h(t) mIT, this system can be written as y' = Ay Find the eigenvectors and eigenvalues of A. Label the eigenvectors xi through x4 in order from largest eigenvalue 4. 4 to smallest (the smallest being negative Scale each eigenvector so that its first component is 1. When you have done so, identify the eigenvector whose fourth component is the largest. What is that largest fourth component? ,-41 16 16 m, 45 Putting the four populations into a vector y() = [s() f(t) h(t) mIT, this system can be written as y' = Ay Find the eigenvectors and eigenvalues of A. Label the eigenvectors xi through x4 in order from largest eigenvalue 4. 4 to smallest (the smallest being negative Scale each eigenvector so that its first component is 1. When you have done so, identify the eigenvector whose fourth component is the largest. What is that largest fourth component