Explore matrix systems of first-order equations and their diagonalization using eigenvectors and eigenvalues in this 48-minute lecture. Delve into higher-order linear ODEs, characteristic equations, and matrix systems of first-order equations. Access accompanying notes and MATLAB code for practical implementation. Part of the ME564 course, this lecture covers introduction to general eigenvalues, systems of differential equations, and general systems of equations. Enhance your understanding of these mathematical concepts crucial for engineering and applied mathematics.