Instructions
- First, you should watch the concepts videos below explaining the topics in the section.
- There are no exercises in this section, but you can see the exercises in Sections 8, 9, and 11, which include finding the fundamental matrix.
- Last, you should attempt to answer the self-assessment questions to determine how well you learned the material.
- When you have finished the material below, you can start on the next section or return to the main differential equations page.
Concepts
- Definition of a fundamental matrix for a system of equations
- Properties of a fundamental matrix
Exercises
Directions: See the exercises in Sections 8, 9, and 11. Those videos all solve system of equations, and then show how to find the fundamental matrix for the system.
Self-Assessment Questions
Directions: The following questions are an assessment of your understanding of the material above. If you are not sure of the answers, you may need to rewatch the videos.
- How is a fundamental matrix of a linear homogeneous system of ODEs defined? Is it an invertible matrix? What is the determinant called?
- How do you write the general solution of the system if you have a fundamental matrix for it?
- What is the special fundamental matrix of an IVP system of ODEs set up at \(t=t_0\)? What is its value at \(t_0\)?