# Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case)

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Lesson Summary:

In this lesson, we learn a more efficient way of solving systems of ODEs through matrices. The lecturer revisits a system of equations dealing with the chilling of a boiled egg, and instead of using elimination to solve it, he uses matrices. By reducing the problem of calculus of differential equations to solving algebraic equations, the lecturer reduces the calculus to algebra. The essential point is to view variables as not equal, and to focus on certain variables while demoting others to the background. By using the fundamental theorem of linear equations, the lecturer finds a condition on lambda, and from there, he is able to solve the system.

Lesson Description:

Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case) -- Lecture 25. Learn a more efficient way of solving systems of ODEs.

Arthur Mattuck, 18.03 Differential Equations, Spring 2006. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 27, 2008). License: Creative Commons BY-NC-SA.