# Math 224-01: Differential Equations: Reading Homework 7.5

1. Undriven Linear Systems with Constant Coefficients : what is the compact form for a general linear system?
1. Operators : what is the linear operator defined in this section? how is it related to the principle of superposition?
2. General solutions : how can we write the general solution of a linear system?
3. Solving linear systems : what is the method that we use to solve a linear system? what do we guess for this? how is this related to an eigenvalue problem?
1. solutions : how are the eigenvectors and eigenvalues of the coefficient matrix related to the solution of an unforced linear system?
2. general solution, nondeficient eigenspaces : what is the general solution of a linear system with nondeficient eigenspaces?
3. deficient eigenspaces : what problem do we encounter when we have a coefficient matrix with deficient eigenspaces? what are the solutions of the system in this case?

Math 224-01: Differential Equations: Reading Homework 7.5