advertisement

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.