MAD4401ReviewTest3

MAD4401ReviewTest3 - MAD 4401 Review for Test 3 James...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
MAD 4401 Review for Test 3 James Keesling April 10, 2009 1 Linear Ordinary Differential Equations Problem 1.1. Let A be an n × n matrix. Define exp( tA ) . Problem 1.2. Let A = ± 1 2 1 0 ² and compute exp( tA ) . Problem 1.3. Let x ( t ) = x 1 ( t ) x 2 ( t ) . . . x n ( t ) and suppose that A is an n × n matrix with constant entries. Consider the following differential equation. dx dt = Ax Show that the general solution of this equation is given by the formula x ( t ) = exp( tA ) · C 1 . . . C n . Problem 1.4. Solve the following differential equation using matrix methods. d 2 x dt 2 + 2 dx dt - 3 x = 0 Problem 1.5. Solve the following differential equation dx dt = Ax for the following A . A = ± 1 1 0 2 ² 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 Vector and Matrix Norms Problem 2.1. Give the definition of a norm on an n - dimensional vector space. Problem 2.2. For any two norms || x || 1 and || x || 2 on the n - dimensional vector space V there are positive numbers r
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 3

MAD4401ReviewTest3 - MAD 4401 Review for Test 3 James...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online