Logo
Home Study Material Contact Search
AI Chat FREE
  1. mathematics
  2. basic math
  3. (3) let v be a vector space over a field f. suppos

(3) Let V be a vector space over a field F. Suppose that a ?...

50.1K

Verified Solution

Question

Basic Math

(3) Let V be a vector space over a field F. Suppose that a ? F,v ? V and av = 0. Prove that a = 0 or v = 0.

(4) Prove that for any field F, F is a vector space over F.

(5) Prove that the set V = {a0 + a1x + a2x 2 + a3x 3 | a0, a1,a2, a3 ? R} of polynomials of degree ? 3 is a vector space over R(with respect to the usual addition and scalar multiplication ofpolynomials).

Answer & Explanation Solved by verified expert
4.4 Ratings (608 Votes)
    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

Chemistry
1.2K views

How does changing the solvent polarity affect reactant vs product stability? Can you justify these observations based...

Biology
1.2K views

1. In what part of a hepatocyte would a drug interaction involving CYP enzymes most likely occur? A....

Chemistry
1.2K views

Sulfur dioxide (SO2 ) is a gas that is a polluant responsible for acid rain. It...

General Management
1.2K views

Cesar Rego Computers, a Mississippi chain of computer hardware and software retail outlets, supplies both educational...

Physics
1.2K views

questions will be considered for marking first 10 attempted A disc of radius 0 1...

Physics
1.2K views

The equation of particle executing simple harmonic T motion is x 5m sin s t...

Physics
1.2K views

2 Two concentric metallic spherical shells are given equal amount of positive charges Then a...

Accounting
1.2K views

For each Financial Transaction below, identify the effect on the Balance Sheet, Income Statement and...

Accounting
1.2K views

Net Sales: 967250 Cost of goods sold: 631450 Average inventories for the year: 198000 Inventories...

Accounting
1.2K views

Equipment with a cost of $154,078 has an estimated residual value of $7,175 and an...

Finance
1.2K views

Smythe needs to consider the incremental costs of filling the special order. For example, will...

Finance
1.2K views

Simply Steak recently expanded its menu at their premier Miami location by offering the new...