Solution Found!

Physics / Classical Mechanics 0 / Chapter 11 / Problem 11.33

Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor

Change Question

The eigenvectors a(1) and a(2) that describe the motion in

Chapter 11, Problem 11.33

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

The eigenvectors a(1) and a(2) that describe the motion in the two normal modes of the two carts of Section 11.2 are given in (11.78). Prove that any (2 x 1) column x can be written as a linear combination of these two eigenvectors; that is, a(1) and a(2) are a basis of the space of (2 x 1) columns.

Questions & Answers

QUESTION:

The eigenvectors a(1) and a(2) that describe the motion in the two normal modes of the two carts of Section 11.2 are given in (11.78). Prove that any (2 x 1) column x can be written as a linear combination of these two eigenvectors; that is, a(1) and a(2) are a basis of the space of (2 x 1) columns.

ANSWER:

Step 1 of 4

A mathematical theorem says that a set of vectors is a basis of a -dimensional vector space if and only if the vectors are linearly independent Another theorem says that a set of vectors is linearly independent if and only if for .

Study Tools You Might Need

Chapter: Problem: 4

Fundamentals of Physics 10
In the return stroke of a typical lightning bolt, a current of 2.5 ' 104 A exists for 20 ms. How much charge is transferred in this event?

Chapter: 2 Problem: 2-10

Engineering Mechanics: Statics 14
Determine the magnitude of the resultant force and its direction, measured counterclockwise from the positive x axis.

Chapter: 13 Problem: 13.2

Elementary Principles of Chemical Processes 3
Five percent excess air is used in burning the reformer fuel; it is drawn into the system at 30C and 70% relative humidity. Estimate the average molecular weight of the air. Why does it differ from the value of 29 determined in Example 3.3-4 even though the ratio of nitrogen to oxygen is the same? De

Chapter: 2 Problem: 38

Holt Physics: Student Edition 2009 1
Two cars travel westward along a straight highway, one at a constant velocity of 85 km/h, and the other at a constant velocity of 115 km/h. a. Assuming that both cars start at the same point, how much sooner does the faster car arrive at a destination 16 km away? b. How far must the cars travel for t

Chapter: 8 Problem: 8-4

Glencoe Accounting: First Year Course, Student Edition 1
Preparing a Six-Column Work Sheet The ending balances in the general ledger accounts of Wilderness Rentals for the period ended May 31 follow. Instructions Prepare a work sheet for the period ended May 31. 1. Write the heading on the work sheet. 2. List all of the accounts in the Account Name

Chapter: 0 Problem: 1

Krugman's Economics for AP® (High School) 2
In each of the following cases, state whether the income effect, the substitution effect, or both are significant. In which cases do they move in the same direction? In opposite directions? Why? a. Orange juice represents a small share of Clares spending. She buys more lemonade and less orange juice

Chapter: 2 Problem: 4

Concepts of Biology 1
An isotope of sodium (Na) has a mass number of 22. How many neutrons does it have? a. 11 b. 12 c. 22 d. 44

Chapter: 6 Problem: 1

Marketing Management 5
When you get your hair cut, what's the "core" of what you buy vs. what are the "value-addeds" in the purchase? What's a consultant's core vs. value-addeds? What are the core vs. value-addeds for music?

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account