ELEMENTS OF MODERN ALGEBRA8th EditionGilbert Publisher: CENGAGE LISBN: 9780357671139
ELEMENTS OF MODERN ALGEBRA
Solutions for ELEMENTS OF MODERN ALGEBRA
Problem 1TFE:
Label each of the following statements as either true or false. Matrix addition is a binary...Problem 2TFE:
Label each of the following statements as either true or false. Matrix multiplication is a binary...Problem 12TFE:
Label each of the following statements as either true or false. Let A be a square matrix of order n...Problem 4E:
Let A=[aij]23 where aij=i+j, and let B=[bij]34 where bij=2ij. If AB=[cij]24, write a formula for cij...Problem 7E:
Let ij denote the Kronecker delta: ij=1 if i=j, and ij=0 if ij. Find the value of the following...Problem 10E:
Find two nonzero matrices A and B such that AB=BA.Problem 11E:
11. Find two nonzero matrices and such that.
Problem 12E:
12. Positive integral powers of a square matrix are defined by and for every positive integer....Problem 18E:
Prove part b of Theorem 1.35.
Theorem 1.35 Special Properties of
Let be an arbitrary matrix...Problem 21E:
Suppose that A is an invertible matrix over and O is a zero matrix. Prove that if AX=O, then X=O.Problem 22E:
Let be the set of all elements of that have one row that consists of zeros and one row of the form...Problem 23E:
Prove that the set S={[abba]|a,b} is closed with respect to matrix addition and multiplication in...Problem 25E:
Let A and B be square matrices of order n over Prove or disprove that the product AB is a diagonal...Browse All Chapters of This Textbook
Chapter 1.1 - SetsChapter 1.2 - MappingsChapter 1.3 - Properties Of Composite Mappings (optional)Chapter 1.4 - Binary OperationsChapter 1.5 - Permutations And InversesChapter 1.6 - MatricesChapter 1.7 - RelationsChapter 2.1 - Postulates For The Integers (optional)Chapter 2.2 - Mathematical InductionChapter 2.3 - Divisibility
Chapter 2.4 - Prime Factors And Greatest Common DivisorChapter 2.5 - Congruence Of IntegersChapter 2.6 - Congruence ClassesChapter 2.7 - Introduction To Coding Theory (optional)Chapter 2.8 - Introduction To Cryptography (optional)Chapter 3.1 - Definition Of A GroupChapter 3.2 - Properties Of Group ElementsChapter 3.3 - SubgroupsChapter 3.4 - Cyclic GroupsChapter 3.5 - IsomorphismsChapter 3.6 - HomomorphismsChapter 4.1 - Finite Permutation GroupsChapter 4.2 - Cayley’s TheoremChapter 4.3 - Permutation Groups In Science And Art (optional)Chapter 4.4 - Cosets Of A SubgroupChapter 4.5 - Normal SubgroupsChapter 4.6 - Quotient GroupsChapter 4.7 - Direct Sums (optional)Chapter 4.8 - Some Results On Finite Abelian Groups (optional)Chapter 5.1 - Definition Of A RingChapter 5.2 - Integral Domains And FieldsChapter 5.3 - The Field Of Quotients Of An Integral DomainChapter 5.4 - Ordered Integral DomainsChapter 6.1 - Ideals And Quotient RingsChapter 6.2 - Ring HomomorphismsChapter 6.3 - The Characteristic Of A RingChapter 6.4 - Maximal Ideals (optional)Chapter 7.1 - The Field Of Real NumbersChapter 7.2 - Complex Numbers And QuaternionsChapter 7.3 - De Moivre’s Theorem And Roots Of Complex NumbersChapter 8.1 - Polynomials Over A RingChapter 8.2 - Divisibility And Greatest Common DivisorChapter 8.3 - Factorization In F [x]Chapter 8.4 - Zeros Of A PolynomialChapter 8.5 - Solution Of Cubic And Quartic Equations By Formulas (optional)Chapter 8.6 - Algebraic Extensions Of A Field
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More Editions of This Book
Corresponding editions of this textbook are also available below:
EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 9780100475755
Elements Of Modern Algebra
8th Edition
ISBN: 9781285463230
EBK ELEMENTS OF MODERN ALGEBRA
8th Edition
ISBN: 8220100475757
Elements Of Modern Algebra
8th Edition
ISBN: 9781285965918
Elements of Modern Algebra
5th Edition
ISBN: 9780534373511
Elements of Modern Algebra
6th Edition
ISBN: 9780534402648
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