- 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

- 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 x_{k}?

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

- When do we die off along y=1/2 x?

a) never

b) always

c) for most starting positions

d) only when a_{1}=0

e) only when a_{2}=0

- Could we write out an eigenvector decomposition for a reflection
matrix (ie are there 2 linearly independent eigenvectors that span
R
^{2})?

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

- Could we write out an eigenvector decomposition for a projection
matrix (ie are there 2 linearly independent eigenvectors that span
R
^{2})?

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

- Could we write out an eigenvector decomposition for a horizontal shear
matrix (ie are there 2 linearly independent eigenvectors that span
R
^{2})?

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)