Solution-Subspaces of a finite dimensional vector space

Subspaces of a finite dimensional vector space

Reference no: EM131038015

Let U, V ⊂ W be subspaces of a finite dimensional vector space W . Define U + V = {w ∈ W | w = u + v, u ∈ U, v ∈ V }.

(a) Prove that dim(U + V ) ≤ dim U + dim V .

(b) Give an example where the inequality in (a) is strict.

Reference no: EM131038015

Questions Cloud

What are the four new management processes : According to our text (HBR, 2011), “Managers using the balanced scorecard do not have to rely on short-term financial measures as the sole indicators of the company’s performance. What are the four new management processes? How can these processes be..

Double declining balance method : Prepare a schedule showing the annual depreciation and end of year accumulated depreciation for the first three years of the assets life under the straight line method, the sum of the years digits method and the double declining balance method.

Defining what constitutes the american nation : For this paper, you will explore the complicated nature of the American nation from 1607 to 1877 by focusing on one of the following groups and examine how their changing roles reflected the limitations and contradictions of the term "of the peopl..

Quantitative model typically used by decision support system : Which of the following is a quantitative model typically used by a Decision Support System or DSS:

Subspaces of a finite dimensional vector space : Let U, V ⊂ W be subspaces of a finite dimensional vector space W . Define U + V = {w ∈ W | w = u + v, u ∈ U, v ∈ V }. (a) Prove that dim(U + V ) ≤ dim U + dim V .

Unfavorable judgment or opinion toward an individual : Prejudice is a favorable or unfavorable judgment or opinion toward an individual or group based on one’s perception of a group, individual, or situation. In detail, provide an example of a scenario in which an employee might feel as though he or she ..

Domain of a combined function : Describe 3 factors that influence the domain of a combined function. Give an example of each.

The customer demand is no longer constant : As the head of a tire shop it is your responsibility to minimize the cost of inventory for thes hop. You decide to focus on one brand of costly tire that costs you $90 per unit. To maintain the tire in the shop, you incur a cost of 25% of the tire pr..

Profit or loss in transaction and express : A trader at Texas buys a television for $7000 from Florida and sells it in Texas for $7600. If his overhead expenses amount to $1000; find his profit or loss in this transaction and express it as percent.

User Account

All Pages

Subspaces of a finite dimensional vector space

Reference no: EM131038015

Reference no: EM131038015

Questions Cloud

Reviews

Write a Review

Mathematics Questions & Answers

Questions on ferris wheel

Logistic map

Finding the probability of cards

Systems of ode

Derive the boolean expression

System of equations

Linear programming problem

Find the natural domain

Introduction to numerical methods

Chart of the topological manifold

Mathematics in computing

Complex problems

Assured A++ Grade

Academics

Major Subjects

Majors

Get In Touch

TERMS & POLICIES

HELP & SUPPORT