# Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters

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Lesson Summary:

In this lesson, we learned about inhomogeneous systems of ODEs using matrix methods. The fundamental matrix, which is a matrix whose columns are two independent solutions, was introduced and its properties were discussed. One important property is that its determinant is never zero for any value of t, and the other property is that it satisfies a matrix differential equation, which is a way of saying that its two columns are solutions to the original system. Finally, we looked at an example of how to use these methods to solve inhomogeneous systems.

Lesson Description:

Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters -- Lecture 28. Learn about inhomogeneous systems of ODEs by using matrices.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 29, 2008). License: Creative Commons BY-NC-SA.