For which n xm matrices A does the equationdim(ker(A)) = dim(ker(A7)) hold? Explain.

FIRST-ORDER SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS I: Introduction and Linear Systems David Levermore Department of Mathematics University of Maryland 23 April 2012 Because the presentation of this material in lecture will diﬀer from that in the book, I felt that notes that closely follow the lecture presentation might be appreciated. Contents 1. Introduction 1.1. Normal Form and Solutions 2 1.2. Initial-Value Problems 3 1.3. Recasting Higher-Order Problems as First-Order Sy