1. If the column vector a=Matrix([[a1],[a2],...,,[an]]) is a nontrivial eigenvector for A, as outputed by Maple, then A has at least the eigenvectors as follows:
   a) all of Rⁿ
   b) an entire line through the origin in Rⁿ
   c) just a and the 0 vector
   d) just a
   e) a and a second vector b that Maple outputs
   
   
   
   
2. If the reduced augmented matrix for the system (A-lambdaI)x=0 is Matrix([[0,0,0],[0,0,0]]) then the (real) eigenvectors of A are:
   a) Just the 0 vector works
   b) A line through the origin
   c) All of R²
   d) A subspace of R³ (with 3 coordinates)
   e) None of the above
   
   
   
   
   
   
3. How many linearly independent eigenvectors does Matrix([[cos(pi),-sin(pi)],[sin(pi),cos(pi)]]) have?
   a) 0
   b) 1
   c) 2
   d) infinite
   e) none of the above
   
   
   
   
4. An eigenvector allows us to turn:
   a) Matrix multiplication into matrix addition
   b) Matrix addition into matrix multiplication
   c) Matrix multiplication into scalar multiplication
   d) Matrix addition into scalar multiplication
   e) none of the above
   
   
   
   
5. How many non-trivial real eigenvectors does Matrix([[cos(pi),-sin(pi)],[sin(pi),cos(pi)]]) have?
   a) 0
   b) 1
   c) 2
   d) infinite
   e) none of the above
   
   
   
   
6. How many nontrivial real eigenvectors does Matrix([[cos(pi/2),-sin(pi/2)],[sin(pi/2),cos(pi/2)]]) have
   a) 0
   b) 1
   c) 2
   d) infinite
   e) none of the above
   
   
   
   
7. Given a square matrix A, to solve for eigenvalues and eigenvectors
   a) (A-lambdaI)x=0 is equivalent, so, since we are looking for nontrivial x solutions, that means that this homogeneous system must have infinite solutions, so we can solve for det(lambdaI- A)=0.
   b) Once we have a lambda that works, we can take the inverse of (A-lambdaI) to solve for the eigenvectors
   c) Once we have a lambda that works, we can create the augmented matrix [A-lamdbaI|0] and reduce to solve for solutions and write out a basis.
   d) a and b
   e) a and c
   
   
   
   
   
   
8. We execute
   A := Matrix([[21/40,3/20],[-3/16,39/40]]);
   Eigenvectors(A);
   in Maple. For most initial conditions of owls and squirrels, what happens to the system in the longterm?
   a) tends to the 0 vector in the ratios of 2 owls to 1 squirrel
   b) tends to the 0 vector in the ratios of 1 owl to 2 squirrels
   c) tends to the 0 vector in the ratios of 2 owls to 5 squirrels
   d) tends to the 0 vector in the ratios of 5 owls to 2 squirrels
   e) other longterm behavior

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9. Is Matrix([[cos(pi),-sin(pi)],[sin(pi),cos(pi)]]) diagonalizable?
   a) yes
   b) no
   
   
   
   
10. Is Matrix([[1,k],[0,1]]) diagonalizable?
    a) yes
    b) no