1. The eigenvector decomposition for a system of owls (x-value) and wood rats (y-value) is given via Which of the following is true about the populations in the longterm for most starting positions?
a) The owls (x-value) dominate
b) The wood rats (y-value) dominate
c) The owl population crashes faster than the wood rats
d) More than one of the above
e) None of the above

2. The eigenvector decomposition for a system of owls (x-value) and wood rats (y-value) is given via Which of the following is true about the trajectory of xk?
a)For most starting positions, the owls die off along y=x but the wood rats don't
b)For most starting positions, the wood rats die off along y=x but the owls don't
c)For most starting positions, the owls and wood rats die off in the ratio of 2 owls to 1 wood rat along y=1/2 x
d)For most starting positions, the owls and wood rats die off in the ratio of 1 owl to 1 wood rat along y=x
e)None of the above

3. When do we die off along y=1/2 x? a) never
b) always
c) for most starting positions
d) only when a1=0
e) only when a2=0

4. Could we write out an eigenvector decomposition for a reflection matrix (ie are there 2 linearly independent eigenvectors that span R2)?
a) yes and I can tell you how the eigenvectors relate to the line of reflection
b) yes but I am unsure of what they are
c) no but I am unsure of why not
d) no and I can explain why not

5. Could we write out an eigenvector decomposition for a projection matrix (ie are there 2 linearly independent eigenvectors that span R2)?
a) yes and I can tell you how the eigenvectors relate to the line of projection
b) yes but I am unsure of what they are
c) no but I am unsure of why not
d) no and I can explain why not 6. Could we write out an eigenvector decomposition for a horizontal shear matrix (ie are there 2 linearly independent eigenvectors that span R2)?
a) yes and I can tell you how the eigenvectors relate to the shear
b) yes but I am unsure of what they are
c) no but I am unsure of why not
d) no and I can explain why not

Solutions
1. e)
2. d)
3. e)
4. a)
5. a)
6. d)