Solution Found!

Math / Linear Algebra 4 / Chapter 2.4 / Problem 20

Linear Algebra | 4th Edition | ISBN: 9780130084514 | Authors: Stephen H. Friedberg, Arnold J. Insel, Lawrence E. Spence

Change Question

Let T: V > W be a linear transformation from an n-dimensional vector space V to an

Chapter 2, Problem 20

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Let T: V > W be a linear transformation from an n-dimensional vector space V to an m-dimensional vector space W. Let 0 and 7 be ordered bases for V and W, respectively. Prove that rank(T) = rank(Lyi) and that nullity(T) = nullity (L,i), where A = [T]^. Hint: Apply Exercise 17 to Figure 2.2.

Questions & Answers

QUESTION:

Let T: V > W be a linear transformation from an n-dimensional vector space V to an m-dimensional vector space W. Let 0 and 7 be ordered bases for V and W, respectively. Prove that rank(T) = rank(Lyi) and that nullity(T) = nullity (L,i), where A = [T]^. Hint: Apply Exercise 17 to Figure 2.2.

ANSWER:

Step 1 of 3

Let be a linear transformation from an n dimensional vector space V to an m dimensional vector space W.

Let and be ordered bases for V and W respectively.

To prove that and

Let us consider the linear transformation defined by

Another linear transformation defined by

Study Tools You Might Need

Chapter: 7 Problem: 46P

Introductory Chemistry 5
Write a balanced chemical equation for the reaction of gaseous nitrogen dioxide with hydrogen gas to form gaseous ammonia and liquid water.

Chapter: 4 Problem: 22E

Elementary Statistics: Picturing the World 6
Problem 22E Finding Probabilities Use the probability distribution you made in Exercise to find the probability of randomly selecting an employee whose overtime is (a) two or three hours, (b) three hours or less, and (c) between two and five hours, inclusive. Exercise Overtime Hours The number of o

Chapter: Problem: 13

Myers' Psychology for AP 2
Self-reflective introspection about the elements of experience best describes a technique used by which school of psychology? a. Darwinists b. Empiricists c. Structuralists d. Behaviorists e. Psychiatrists

Chapter: 15 Problem: PROBLEM 15-11

Organic Chemistry 9
Predict the product(s) of light-initiated reaction with NBS in CCl4 for the following starting materials. (a) cyclopentene (b) 2,3-dimethylbut-2-ene (c) CH3 toluene

Chapter: 25 Problem: 25.18

Organic Chemistry 3
Draw the product of each reaction. a. CH3NH2 NaBH3CN CHO c. (CH3CH2)2NH NaBH3CN O b. O NH3 NaBH3CN d. O NaBH3CN + NH2

Chapter: 3 Problem: 3.7

Organic Chemistry, 9
Given the following partial structure, add a substituent X to C-1 so that it satisfies the indicated stereochemical requirement What is the ACCX torsion (dihedral) angle in each? (a) Anti to A (c) Anti to C-3 A 3 1 (b) Gauche to A (d) Gauche to C-3

Chapter: 4 Problem: 24

Biology 2e by Openstax
Diseased animal cells may produce molecules that activate death cascades to kill the cells in a controlled manner. Why would neighboring healthy cells also die? a. The death molecule is passed through desmosomes. b. The death molecule is passed through plasmodesmata. c. The death molecule disrupts th

Chapter: 15 Problem: 8

Urban Economics 8
Suppose the marginal value of a square foot of factory space is constant at $1.00. The marginal benefit of a square foot of housing space is $1.00 for 1,000 square feet and $0.80 for 1,200 square feet. Suppose the government provides a 20 percent mortgage subsidy, cutting the net price of housing to

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account