Question: Cosets in R3 Using the following definition, in Problems 1 and 2, find the W-cosets for the give vectors v and given a graphical description

Cosets in R3 Using the following definition, in Problems 1 and 2, find the W-cosets for the give vectors v̅ and given a graphical description of each?
Cosets
If W is a subspace of vector space that includes the origin, and; v̅ is a vector in Rn, then the W-coset of v̅, denoted v̅ + W, is the set defined by
v̅ + W = [v̅ + w̅ | w̅ is in W)
Thus, in R3, if W is a plane passing through the origin, then the coset v̅ + W is a plane parallel to W passing through v̅?
1. W = {[x1, x2, x3] | x1 + x2 + x3 = 0}; v̅ = (0, 0, 1)
2. W = {[x1, x2, x3] | x3 = 0};v̅ = (1, 1, 1)

Step by Step Solution

★★★★★

3.34 Rating (175 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

1 Cosets in R 3 W W x 1 x 2 x 3 x 1 x 2 x 3 0 v 0 0 1 We want to write W in parame... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

947-M-L-A-L-S (4813).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3. The trace of an n x n matrix A = [aij], denoted Tr A, is the sum of the diagonal elements: 1....

Orthogonal Complements: Prove the properties stated in Problems 1-2 using the following definition, illustrated by Fig. 3.5.4. Assume that V is a subspace of Rn. Let V be a subspace of Rn. A vector...

Using Definition 3.1, prove that each of the following limits exists. a) b) c) d) lim x2 +2x-5=3 x2+x-2 lim = 3 lim x3 + 2x + 1 = 4 lim x3 sin(er) = 0

MINI-PROJECT Implement a Software-Engineering Process stages by selecting any topic which is mention below or you can select your desired any other topic. Website Administration Airport checking-in...

Finance Female Male Male Male Male Male Male Male Male Female Male Female Female Male Male Female Male Female Male Male Male Male Female Male Female Male Male Male Female Male Male Female Female Male...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

uantitative Analysis BA 452 Homework 3 Questions Homework 3 covers the theory and applications in Lessons I-6 and I-7. This document has four parts: Objectives of doing your homework. Assignment of...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

1 2.3 Definition of a Discrete Probability Function Definition: Let S be a discrete sample space from some experiment. A function P, defined on all events in S, is said to be a probability function...

An Australian based importer has entered into a US dollar denominated contract that will require payment of US$10,000,000 in one month. The importer wishes to lock in an exchange rate today in order...

1. Who owned the e-mail system that McLaren used? Who established it? 2. What was the purpose of the e-mail system? Why did Microsoft set it up? 3. Why did Microsoft care about the contents of...

What Smucker's 2 0 1 9 profit margin? Was this an improvement over the company's 2 0 1 8 profit margin? Question 3 options: 1 5 . 2 % which was an improvement over 2 0 1 8 ' s profit margin. 6 . 6 %...

What pay level does the efficiency wage predict? Does the theory accurately predict organization behavior? Why or why not?

Any integral of the form x m J n (x) dx can be evaluated in terms of Bessel functions and the indefinite integral J 0 (x) dx. The latter integral cannot be simplified further, but the function x 0...

Derive the recursion formula in Eq. (2) for Bessels equation. [(m + r)2 - p2]cm + Cm-2 = 0 (2)

In Problems 1 through 8, determine whether x = 0 is an ordinary point, a regular singular point, or an irregular singular point. If it is a regular singular point, find the exponents of the...

A corporation in a 40% tax bracket invests in the preferred stock of another company and earns a 5% pretax rate of return. An individual investor in a 20% tax bracket invests in the same preferred...

Notice this study used the verbal answer from each subject to measure the cocaine use status after six weeks of treatment. It has been argued that verbal reporting of cocaine use will cause subjects...

You have the following expectations about market returns and interest rates on T-bills: T-Bill Rate Market Rate Probability RF Probability MR 0.1 0.02 0.1 -0.1 0.2 0.03 0.3 0.15 0.4 0.06 0.3 0.33 0.2...