{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# The equations reduce to the single equation and a

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

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ____________________________________ page 409 —————————————————————————— CHAPTER 7. —— I A It can be shown that the partial sums on the left hand side converge for all . Taking the limit as on both sides of the equation, we obtain A Alternatively, consider the system x Ax . Since ODEs are uncoupled, the vectors x e , are a set of linearly independent solutions. Hence the matrix X e e is a fundamental matrix. Finally, since X e e I , it follows that e e 17 . Assuming that x is a solution, then both sides of the equation to obtain A. A , with A x Integrate . Hence x A . . Proceed with the iteration x With A . x , and noting that A is a constant matrix, ________________________________________________________________________ page 410 —————————————————————————— CHAPTER 7. —— x Ax x That is, I Ax A x. . We then have x AI x Ax I A Ax Ax A x. Now suppose that I A A A A A x. It follows that AI AI A A A x A A A A A x x Therefore I A By induction, the asserted form of . Define lim A A x. is valid for all . It can be shown that the...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online