Sketch a sadle
(10 points)
Open this webpage one more time and refer to the last section entitled "Sketch a saddle" to get one more system.
The system should have two real eigenvalues with unequal signs. Find those eigenvalues with their corresponding eigenvectors and use that information to sketch the phase plane by hand. Your sketch should include the eigenvectors and four solutions. Snap a picture and upload.
Note that you can use code like the following in the sage cell server to compute eigensystems:
from scipy.linalg import eig eig([[-1,4],[4,-1]]) # OUT: # (array([ 3.+0.j, -5.+0.j]), # array([[ 0.70710678, -0.70710678], # [ 0.70710678, 0.70710678]]))
Comments
My system was
$$
\begin{align}
x' &= -7x \\
y' &= x + 9y
\end{align}
$$
$$
\begin{align}
x' &= 6x + 0y \\
y' &= -6x - 5y
\end{align}
$$
@sara,@austin,@shp700
Could you be a bit more clear about the locations of your eigenvectors, please?