Matrix Systems of Differential Equations

Learn how to transform high-order linear differential equations into matrix systems of first-order differential equations in this 25-minute video lecture. Explore the process of introducing new variables, writing equations as matrix systems, and understand how eigenvalues of the matrix system relate to the roots of the characteristic polynomial. Gain insights into solving general ODEs using eigenvalues and eigenvectors, leveraging the power of linear algebra. Follow along with a practical example of a 3x3 matrix system of ODEs to reinforce your understanding of this crucial step in differential equation analysis.

Overview
Introduce New Variables
Writing as Matrix System of Equations
Summary and Takeaways
Eigenvalues of Matrix System are Roots of the Characteristic Polynomial
Example 3x3 Matrix System of ODEs