Linear Algebra A Modern Introduction 4th Edition David Poole Solutions Manual
Complete Solution Manual Linear Algebra A Modern Introduction 4th Edition David Poole
PDF File
All Pages
All Chapters
Grade A+
linear algebra a modern introduction 4th edition d
linear algebra a modern introduction
Gekoppeld boek
Titel boek:
Auteur(s):
Uitgave:
ISBN:
Druk:
Meer samenvattingen voor studieboek
Solutions Manual for Linear Algebra A Modern Introduction 4th Edition by David Poole 2024 . All Chapters A+
Vector en matrix rekenen
Samenvatting Linear Algebra, ISBN: 9781285463247 Lineaire Algebra (5082LIAL6Y)
Alles voor dit studieboek
(11)
Geschreven voor
Linear Algebra
Linear Algebra
3
beoordelingen
Door: hadrienhebert • 5 maanden geleden
Door: agaathdevries3 • 10 maanden geleden
Door: gradexam • 10 maanden geleden
We sincerely appreciate your outstanding 5-star review of this document. Your feedback means a great deal to us!

Door: piyachat • 10 maanden geleden
useless
Verkoper
Volgen
gradexam
Ontvangen beoordelingen
Voorbeeld van de inhoud
Linear Algebra A Modern Introduction 4th Edition David Poole Solutions Manual Contents 1 Vectors 3 1.1 The Geometry and Algebra of Vectors ................................ ................................ ................................ ...... 3 1.2 Length and Angle: The Dot Product ................................ ................................ ................................ . 10 Exploration: Vectors and Geometry ................................ ................................ ................................ .................. 25 1.3 Lines and Planes ................................ ................................ ................................ ................................ ......... 27 Exploration: The Cross Product ................................ ................................ ................................ ................. 41 1.4 Applications ................................ ................................ ................................ ................................ ................. 44 Chapter Review ................................ ................................ ................................ ................................ .................... 48 2 Systems of Linear Equations 53 2.1 Introduction to Systems of Linear Equations ................................ ................................ .......................... 53 2.2 Direct Methods for Solving Linear Systems ................................ ................................ ............................. 58 Exploration: Lies My Computer Told Me ................................ ................................ ................................ .. 75 Exploration: Partial Pivoting ................................ ................................ ................................ ....................... 75 Exploration: An Introduction to the Analysis of Algorithms ................................ ................................ .......... 77 2.3 Spanning Sets and Linear Independence ................................ ................................ ................................ .79 2.4 Applications ................................ ................................ ................................ ................................ ................. 93 2.5 Iterative Methods for Solving Linear Systems ................................ ................................ ...................... 112 Chapter Review ................................ ................................ ................................ ................................ ................. 123 3 Matrices 129 3.1 Matrix Operations ................................ ................................ ................................ ................................ .... 129 3.2 Matrix Algebra ................................ ................................ ................................ ................................ .. 138 3.3 The Inverse of a Matrix ................................ ................................ ................................ .......................... 150 3.4 The LU Factorization ................................ ................................ ................................ ......................... 164 3.5 Subspaces, Basis, Dimension, and Rank ................................ ................................ ................................ 176 3.6 Introduction to Linear Transformations ................................ ................................ ................................ 192 3.7 Applications ................................ ................................ ................................ ................................ .............. 209 Chapter Review ................................ ................................ ................................ ................................ ................. 230 4 Eigenvalues and Eigenvectors 235 4.1 Introduction to Eigenvalues and Eigenvectors ................................ ................................ ..................... 235 4.2 Determinants ................................ ................................ ................................ ................................ ............ 250 Exploration: Geometric Applications of Determinants ................................ ................................ ................ 263 4.3 Eigenvalues and Eigenvectors of n × n Matrices ................................ ................................ ................. 270 4.4 Similarity and Diagonalization ................................ ................................ ................................ ......... 291 4.5 Iterative Methods for Computing Eigenvalues ................................ ................................ ..................... 308 4.6 Applications and the Perron -Frobenius Theorem ................................ ................................ ................ 326 Chapter Review ................................ ................................ ................................ ................................ ................. 365 1 2 CONTENTS 5 Orthogonality 371 5.1 Orthogonality in Rn................................ ................................ ................................ ................................ ................................ .......... 371 5.2 Orthogonal Complements and Orthogonal Projections ................................ ................................ ....... 379 5.3 The Gram -Schmidt Process and the QR Factorization ................................ ................................ .. 388 Exploration: The Modified QR Process ................................ ................................ ................................ ... 398 Exploration: Approximating Eigenvalues with the QR Algorithm ................................ ......................... 402 5.4 Orthogonal Diagonalization of Symmetric Matrices ................................ ................................ ............ 405 5.5 Applications ................................ ................................ ................................ ................................ ............... 417 Chapter Review ................................ ................................ ................................ ................................ .................. 442 6 Vector Spaces 451 6.1 Vector Spaces and Subspaces ................................ ................................ ................................ ................. 451 6.2 Linear Independence, Basis, and Dimension ................................ ................................ ......................... 463 Exploration: Magic Squares ................................ ................................ ................................ ............................. 477 6.3 Change of Basis ................................ ................................ ................................ ................................ ........ 480 6.4 Linear Transformations ................................ ................................ ................................ ............................ 491 6.5 The Kernel and Range of a Linear Transformation ................................ ................................ ............. 498 6.6 The Matrix of a Linear Transformation ................................ ................................ ................................ 507 Exploration: Tiles, Lattices, and the Crystallographic Restriction ................................ ........................ 525 6.7 Applications ................................ ................................ ................................ ................................ ............... 527 Chapter Review ................................ ................................ ................................ ................................ .................. 531 7 Distance and Approximation 537 7.1 Inner Product Spaces ................................ ................................ ................................ ............................... 537 Exploration: Vectors and Matrices with Complex Entries ................................ ................................ ...... 546 Exploration: Geometric Inequalities and Optimization Problems ................................ .............................. 553 7.2 Norms and Distance Functions ................................ ................................ ................................ ............... 556 7.3 Least Squares Approximation ................................ ................................ ................................ ................. 568 7.4 The Singular Value Decomposition ................................ ................................ ................................ ........ 590 7.5 Applications ................................ ................................ ................................ ................................ ............... 614 Chapter Review ................................ ................................ ................................ ................................ .................. 625 8 Codes 633 8.1 Code Vectors ................................ ................................ ................................ ................................ ............. 633 8.2 Error -Correcting Codes ................................ ................................ ................................ ........................... 637 8.3 Dual Codes ................................ ................................ ................................ ................................ ................ 641 8.4 Linear Codes ................................ ................................ ................................ ................................ ............. 647 8.5 The Minimum Distance of a Code ................................ ................................ ................................ ......... 650 −3 0 −3 −3 3 0 −3 3 0 −3 −2 −5 Chapter 1 Vectors 1.1 The Geometry and Algebra of Vectors 1. 2. Since 2 + 3 = 5 , 2 + 2 = 4 , 2 + −2 = 0 , 2 + 3 = 5 , plotting those vectors gives – – – – – 3 (–2, 3) 3 (2, 3) 2 1 –2 –1 1 2 (3, 0) 3 –1 (3, –2) –2 1 2 3 4 5 1 c b 2 a 3 d 4 5 4 CHAPTER 1. VECTORS #−−−−» — − − 2 2 2 2 6 3 2 3 6 6 #−−−−» 3 2 a 1 c b d –1 1 2 3 3. c 4. Since the heads are all at (3, 2, 1), the tails are at 3 0 3 3 3 0 3 1 2 3 −1 4 2 − 2 = 0 , 2 − 2 = 0 , 2 − −2 = 4 , 2 − −1 = 3 . 1 0 1 #−−−−» 1 1 0 1 1 0 1 −2 3 5. The four vectors AB are – – In standard position, the vectors are #−−−−» (a) AB = [4 1, 2 ( 1)] = [3, 3]. #−−−−» (b) AB = [2 − 0, −1 − (−2)] = [2, 1] (c) AB = 1 − 2, 3 − 3 = − 3 , 3 (d) AB = 1 − 1 , 1 − 1 = − 1 , 1 . 2 z 1 b –2 –1 0 1 y 2 0 –1 0 1 a 2 3 x –1 d –2 3 c 2 1 d a 1 2 3 4 1 b 2
Voordelen van het kopen van samenvattingen bij Stuvia op een rij:
Verzekerd van kwaliteit door reviews
Stuvia-klanten hebben meer dan 700.000 samenvattingen beoordeeld. Zo weet je zeker dat je de beste documenten koopt!
Snel en makkelijk kopen
Je betaalt supersnel en eenmalig met iDeal, creditcard of Stuvia-tegoed voor de samenvatting. Zonder lidmaatschap.
Focus op de essentie
Samenvattingen worden geschreven voor en door anderen. Daarom zijn de samenvattingen altijd betrouwbaar en actueel. Zo kom je snel tot de kern!
Veelgestelde vragen
Wat krijg ik als ik dit document koop?
Je krijgt een PDF, die direct beschikbaar is na je aankoop. Het gekochte document is altijd, overal en oneindig toegankelijk via je profiel.
Tevredenheidsgarantie: hoe werkt dat?
Onze tevredenheidsgarantie zorgt ervoor dat je altijd een studiedocument vindt dat goed bij je past. Je vult een formulier in en onze klantenservice regelt de rest.
Van wie koop ik deze samenvatting?
Stuvia is een marktplaats, je koop dit document dus niet van ons, maar van verkoper gradexam. Stuvia faciliteert de betaling aan de verkoper.
Zit ik meteen vast aan een abonnement?
Nee, je koopt alleen deze samenvatting voor €16,83. Je zit daarna nergens aan vast.