Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. determine whether or not w is a subspace of r3 whe

Determine whether or not W is a subspace of R3 where W consists of all vectors...

60.1K

Verified Solution

Question

Basic Math

Determine whether or not W is a subspace of R3 whereW consists of all vectors (a,b,c) in R3 such that

1. a =3b

2. a <= b <= c

3. ab=0

4. a+b+c=0

5. b=a2

6. a=2b=3c

Answer & Explanation Solved by verified expert
4.3 Ratings (878 Votes)
Let X abc and Y def be 2 arbitrary vectors in W and let k be an arbitrary scalar 1 We have a 3b and d 3e so that XY 3bbc3eef 3bebecf This implies that XY W so that W is closed under vector addition Also kX k 3bbc 3kbkbkc This implies that kX W so that W is closed under scalar multiplication Further since 30 0 hence the zero vector000 W Therefore W is a    See Answer
Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:
  • Unlimited Question Access with detailed Answers
  • Zin AI - 3 Million Words
  • 10 Dall-E 3 Images
  • 20 Plot Generations
  • Conversation with Dialogue Memory
  • No Ads, Ever!
  • Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!
Become a Member

Other questions asked by students

Q

Given 21 22 which similarity criteria proves that AABN AYXN Justify your thinking T B...

Geometry
Q

What is a water pump? Why is it important? Give an example with details where a...

Mechanical Engineering
Q

Take the Laplace transform of the following initial value and solve for Y(s)=L{y(t)}: y??+4y={sin(?t) ,0, 0?t<11?t y(0)=0,y?(0)=0 Y(s)=...

Advance Math
Q

Spolls system Nullification crisis Indian Removal Act Which president is most associated with these terms...

Biology
Q

9 2 What Did One Dog Say To The Other Dog Write the letter of...

Calculus
Q

K For the polynomial funct turning points on the gra f x x 2 x...

Algebra
Q

Solve the system by substitution.2x + y = 43x + 2y = 1Select one:The solution...

Algebra
Q

Westerville Company reported the following results from last years operations: Sales...

Accounting
Q

Base fixed costs of starting a small cafe in melbourne

Accounting
Q

Additional Information 0 A $33.000 note payable is retired at its $33,000 carrying (book) value...

Accounting
Q

(PLEASE TYPE THE ANSWERS) (ACCOUNTING 640) Explain the how CVP analysis might be used in...

Accounting
Q

The following data are accumulated by Lone Peak Inc. in evaluating two competing capital investment...

Accounting