Substituting into the coefficient matrix the system

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: The fundamental matrix for the system x x is given by Direct multiplication results in ________________________________________________________________________ page 408 —————————————————————————— CHAPTER 7. —— Hence 15 . Let be arbitrary, but fixed, and variable. Similar to the argument in Prob. , the columns of the matrix are linear combinations of fundamental solutions. Hence the columns of are also solution of the system of equations. Further, setting , I That is, is a solution of the initial value problem Z AZ , with Z Now consider the change of variable . Let W Z . The given initial value problem can be reformulated as W Since that AW , with W is a fundamental matrix satisfying A , with I , it follows W That is, . Based on Part W Z . , I . Hence . It also follows that 16. Let A be a diagonal matrix, with A positive integer, , A e e e e e e . Note that for any . It follows, from basic matrix algebra, that ____________________________________...
View Full Document

This note was uploaded on 03/11/2014 for the course MA 303 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.

Ask a homework question - tutors are online