(a) Find a 3×3 matrix A such that 0 is the only eigenvalue of A,
and the space of eigenvectors of 0 has dimension 1. (Hint: upper
triangular matrices are your friend!)
(b) Find the general solution to x' = Ax.
PLEASE SHOW YOUR WORK CLEARLY.
Problem 3:
Find the equilibrium distribution for each transition
matrix.
a)
1/2 1/9 3/10
1/3 1/2 1/5
1/6 7/18 1/2
b)
2/5 0 3/4
0 2/3 1/4
3/5 1/3 0
Problem 4:
For either transition matrix in problem 3, find the other two
eigenvalues with corresponding eigenvectors.
Problem 3:
Find the equilibrium distribution for each transition
matrix.
a)
1/2 1/9 3/10
1/3 1/2 1/5
1/6 7/18 1/2
b)
2/5 0 3/4
0 2/3 1/4
3/5 1/3 0
Problem 4:
For either transition matrix in problem 3, find the other two
eigenvalues with corresponding eigenvectors.