• You must show complete work to earn credit. Open book, Open note.

• You can use the internet, but LIST which resources you used.

This is a direction field plot for the 2 × 2 system X0(t) = AX(t):

1. (5 points) Sketch the two straight-line solutions and label them.

2. (5 points) Explain (in your own words) the connection between straightline solutions, eigenvectors, and the general solution.

3. (5 points) Use the plot to calculate the eigenvectors of A and relate them to your straight-line solutions.

4. (5 points) Explain (in your own words) the signs of the eigenvalues of A. Can you say anything about the relative magnitude of the eigenvalues? The last quesiton is intentionally open-ended. Write down your thought process even if you aren’t sure.