Name:
CSU ID:
Homework 9
April 10, 2015
1. S5.2 ]20
2. S5.2 ]27
3. S5.2 ]32
4. S5.3 ]10
5. S5.3 ]18
6. S5.3 ]26
7. S5.3 ]34
8. S5.3 ] TF
9. Consider the differential equation ~y 0 = A~y with initial condition ~y (0) =
[−3, 4, 1]T . The matrix A given below has eigenvalues λ = 2, −5, 3.
(a) For each eigenvalue, find the eigenvector by bringing λI − A to
RREF. The eigenvector should be defined with integers.
(b) Define a matrices S and D such that S −1 AS = D is a diagonal
matrix with the ordered eigenvalues given in (a).
(c) Solve the differential equation. The solution should be written as
a linear combination of eigenvectors.


4 −4 −2


47
26 
A =  −5
11 −92 −51
10. Rewrite the initial value problem y 00 + 5y 0 + 6y = 0 with initial conditions y(0) = 7, y 0 (0) = 2 in matrix/vector format.