Chapter 10

Plot trajectories of the given system. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}2& -1\\ 1& 0\end{array}\right]\mathbf{y}$$

The matrices of the systems in exercises are singular. Describe and graph the trajectories of nonconstant solutions of the given systems. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}1& -3\\ -1& 3\end{array}\right]\mathbf{y}$$

In Exercises $33-40$ find vectors $\mathbf{U}$ and $\mathbf{V}$ parallel to the axes of symmetry of the shadow trajectories, and plot a typical trajectory. $$\text{ C/G }{\mathbf{y}}^{\prime }=\left[\begin{array}{rr}-1& -5\\ 20& -1\end{array}\right]\mathbf{y}$$

Plot trajectories of the given system. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}-1& -3\\ 3& 5\end{array}\right]\mathbf{y}$$

Plot trajectories of the given system. $${\mathbf{y}}^{\prime }=\left[\begin{array}{ll}-5& 3\\ -3& 1\end{array}\right]\mathbf{y}$$

In Exercises $33-40$ find vectors $\mathbf{U}$ and $\mathbf{V}$ parallel to the axes of symmetry of the shadow trajectories, and plot a typical trajectory. $$\text{ C/G }{\mathbf{y}}^{\prime }=\left[\begin{array}{rr}-7& 10\\ -10& 9\end{array}\right]\mathbf{y}$$

The matrices of the systems in exercises are singular. Describe and graph the trajectories of nonconstant solutions of the given systems. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}1& -2\\ -1& 2\end{array}\right]\mathbf{y}$$

The matrices of the systems in exercises are singular. Describe and graph the trajectories of nonconstant solutions of the given systems. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}-4& -4\\ 1& 1\end{array}\right]\mathbf{y}$$

Plot trajectories of the given system. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}-2& -3\\ 3& 4\end{array}\right]\mathbf{y}$$

The matrices of the systems in exercises are singular. Describe and graph the trajectories of nonconstant solutions of the given systems. $${\mathbf{y}}^{\prime }=\left[\begin{array}{rr}3& -1\\ -3& 1\end{array}\right]\mathbf{y}$$