Trajectories of Linear Systems

Part 2: Complex Eigenvalues

For each of the following systems:

• Record the eigenvalues and eigenvectors.
• Draw enough trajectories to get a comprehensive view of the phase portrait of the system.
• Determine whether trajectories travel clockwise or counterclockwise.
• Explain what features of the eigenvalues correspond to whether trajectories spiral or not -- and if so, whether the spiral is inward or outward.

1. A =
2. A =
3. A =