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 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
   
   
   
   
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)