Calculate the eigenvalues of this matrix:

[Note-- you'll probably want to use a calculator or computer to estimate the roots of the polynomial which defines the eigenvalues. You also may want to view a phase plane plot (right click to open in a new window).] ]

$A = \left[\begin{array}{cc} -45 &15\cr -45 &15 \end{array}\right]$

smaller eigenvalue $=$

associated eigenvector $=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

larger eigenvalue $=$

associated, eigenvector $=$ $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$

---

The solution curves converge to different points on parallel paths.

If $y' = Ay$ is a differential equation, how would the solution curves behave?

A. The solution curves converge to different points on parallel paths.
B. All of the solutions curves would converge towards 0. (Stable node)
C. The solution curves diverge from different points on parallel paths.
D. The solution curves would race towards zero and then veer away towards infinity. (Saddle)
E. All of the solution curves would run away from 0. (Unstable node)

---