Show that a linear map is one-to-one if and only if it preserves linear independence.

Question:

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 02:01 AM

See More Questions

Let V be a normed vector space. Prove that a linear map L: V V defines an isometry of V for the given norm if and only if it maps the unit sphere S1 = {||u|| = 1} to itself: L[S1] = {L[u] | u S1} =...
The first two items of this question are review. (a) Prove that the composition of one-to-one maps is one-to-one. (b) Prove that if a linear map is not one-to-one then at least one nonzero vector...
Show that any linear map is the sum of maps of rank one.
What is the MFD? UFD? How are they related?
Draw a supply-and-demand diagram to explain the effect of a negative externality that occurs as a result of a firms production process.
Describe factors in the external environment that could create uncertainty for Lonely Planet. LO.1
1 What is the main transformation performed in Cameron Balloons?
Is independence impaired for the individual or the public accounting firm on these SEC filing audits according to SEC independence rules? a. CPA Yolanda is the Best & Co engagement partner on the...
What are some articles About Bonds write a short summary about it and how it can relate to 1) Service: Demonstrate Christ's mercy and compassion to others through humility of motive, attitude and...
Bunker Company negotiated a lease with Gilbreth Company that begins on January 1, 2014. The lease term is three years, and the assets economic life is four years. The annual lease payments are...
(a) Prove that a homomorphism is onto if and only if its rank equals the dimension of its codomain. (b) Conclude that a homomorphism between vector spaces with the same dimension is one-to-one if and...
Corollary 2.17 says that for there to be an onto homomorphism from a vector space V to a vector space W, it is necessary that the dimension of W be less than or equal to the dimension of V. Prove...
What is the definition of South and North in the United Nations terminology? How does environmental impact differ in those two major earth regions? What factors are prevalent and where?
Pink Jeep Tours offers off-road tours to individuals and groups visiting the Southwestern U.S. hotspots of Sedona, Arizona, and Las Vegas, Nevada. Take a tour of the companys Web site at...
The following are unrelated accounting practices: 1. Pine Company purchased a new $\$ 30$ snow shovel that is expected to last six years. The shovel is used to clear the firm's front steps during...
Identify whether the following statements are true or false. 1. One argument for IFRS is that there is less globalization in the world. 2. IFRS is accepted as GAAP in every country of the world. 3....
You will need isometric dot paper for this question. Part of a pattern using four rhombuses is drawn on isometric dot paper below. By drawing two more rhombuses, complete the pattern so that it has a...
Fred Flores operates a golf driving range. For each of the following financial items related to his business, indicate the financial statement (or statements) in which the item would be reported:...
Use any method to find the volume of the solid obtained by rotating the region enclosed by the curves about the given axis. x = 4y y 3 , x = 0, y 0, x-axis
Modify the counter from Exercise 5.44 such that the counter will either increment by 4 or load a new 32-bit value, D, on each clock edge, depending on a control signal Load. When Load = 1, the...
In Exercises 9-16, find a basis for the eigenspace corresponding to each listed eigenvalue. 1. 2. [3 2 01,A== 1,3
Find the characteristic polynomial and the real eigenvalues of the matrices in Exercises 1-2. 1. 2. 2 2
For the matrices in Exercises 1-2, list the real eigenvalues, repeated according to their multiplicities. 1. 2. 2625 0330 5200 5000 I 1 0005 0233 3602
September 1 . Purchased a new truck for $ 8 3 , 0 0 0 , paying cash. September 4 . Sold the truck purchased January 9 , Year 2 , for $ 5 3 , 6 0 0 . ( Record depreciation to date for Year 3 for the...
Find the NPV for the following project if the firm's WACC is 8%. Make sure to include the negative in your answer if you calculate a negative. it DOES matter for NPV answers
What is the value of a 10-year, $1,000 par value bond with a 12% annual coupon if its required return is 11%?

Show that a linear map is one-to-one if and only if it preserves linear independence.

Question:

Step by Step Answer:

We are proving that h V W is onetoone if and only if for every linearly independent subset S of V th...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions