# Linear Algebra with Applications 9th edition

Gareth Williams
Publisher: Jones and Bartlett Learning

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• Chapter 1: Linear Equations and Vectors
• 1.1: Matrices and Systems of Linear Equations (8)
• 1.2: Gauss-Jordan Elimination (7)
• 1.3: The Vector Space Rn (9)
• 1.4: Subspaces of Rn (7)
• 1.5: Basis and Dimension (11)
• 1.6: Dot Product, Norm, Angle, and Distance (15)
• 1.7: Curve Fitting, Electrical Networks, and Traffic Flow (9)
• 1: Review Exercises (48)
• 1: Test Bank (28)

• Chapter 2: Matrices and Linear Transformations
• 2.1: Addition, Scalar Multiplication, and Multiplication of Matrices (7)
• 2.2: Properties of Matrix Operations (7)
• 2.3: Symmetric Matrices and Seriation in Archaeology (6)
• 2.4: The Inverse of a Matrix and Cryptography (12)
• 2.5: Matrix Transformations, Rotations, and Dilations (6)
• 2.6: Linear Transformations, Graphics, and Fractals (7)
• 2.7: The Leontief Input-Output Model in Economics (3)
• 2.8: Markov Chains, Population Movements, and Genetics (5)
• 2.9: A Communication Model and Group Relationships in Sociology (5)
• 2: Review Exercises (57)
• 2: Test Bank (31)

• Chapter 3: Determinants and Eigenvectors
• 3.1: Introduction to Determinants (14)
• 3.2: Properties of Determinants (9)
• 3.3: Determinants, Matrix Inverses, and Systems of Linear Equations (10)
• 3.4: Eigenvalues and Eigenvectors (9)
• 3.5: Google, Demography, Weather Prediction, and Leslie Matrix Models (10)
• 3: Review Exercises (50)
• 3: Test Bank (27)

• Chapter 4: General Vector Spaces
• 4.1: General Vector Spaces and Subspaces (6)
• 4.2: Linear Combinations of Vectors (5)
• 4.3: Linear Independence of Vectors (6)
• 4.4: Properties of Bases (11)
• 4.5: Rank (10)
• 4.6: Projections, Gram-Schmidt Process, and QR Factorization (16)
• 4.7: Orthogonal Complement (6)
• 4.8: Kernel, Range, and the Rank/Nullity Theorem (8)
• 4.9: One-to-One Transformations and Inverse Transformations (4)
• 4.10: Transformations and Systems of Linear Equations (2)
• 4: Review Exercises (122)
• 4: Test Bank (34)

• Chapter 5: Coordinate Representations
• 5.1: Coordinate Vectors (11)
• 5.2: Matrix Representations of Linear Transformations (11)
• 5.3: Diagonalization of Matrices (12)
• 5.4: Quadratic Forms, Difference Equations, and Normal Modes (5)
• 5.5: Linear Differential Equations (Calculus Prerequisite) (8)
• 5: Review Exercises (27)
• 5: Test Bank (32)

• Chapter 6: Inner Product Spaces
• 6.1: Inner Product Spaces (12)
• 6.2: Non-Euclidean Geometry and Special Relativity (8)
• 6.3: Approximation of Functions and Coding Theory (13)
• 6.4: Least Squares Solutions (29)
• 6: Review Exercises (18)
• 6: Test Bank (26)

• Chapter 7: Numerical Methods
• 7.1: Gaussian Elimination (9)
• 7.2: The Method of LU Decomposition (22)
• 7.3: Practical Difficulties in Solving Systems of Equations (12)
• 7.4: Iterative Methods for Solving Systems of Linear Equations (7)
• 7.5: Eigenvalues by Iteration and Connectivity of Networks (14)
• 7.6: The Singular Value Decomposition (35)
• 7: Review Exercises (19)
• 7: Test Bank (28)

• Chapter 8: Linear Programming
• 8.1: A Geometrical Introduction to Linear Programming (20)
• 8.2: The Simplex Method (16)
• 8.3: Geometrical Explanation of the Simplex Method (6)
• 8: Review Exercises (8)
• 8: Test Bank (15)

Providing a flexible blend of theory and applications, Linear Algebra with Applications, 9th edition, by Gareth Williams, is designed for the introductory course in linear algebra for students within engineering, mathematics, business management, and physics. Throughout the text the author provides interesting applications, ranging from theoretical applications such as the use of linear algebra in differential equations, to many practical applications in the fields of electrical engineering, traffic analysis, relativity, history, and more. The WebAssign component for this title includes question links to the full eBook along with useful Instructor Resources such as related PowerPoint Slides, a test bank of questions, and the Instructor Solutions Manual.

Use the Textbook Edition Upgrade Tool to automatically update all of your assignments from the previous edition to corresponding questions in this textbook.

## Questions Available within WebAssign

Most questions from this textbook are available in WebAssign. The online questions are identical to the textbook questions except for minor wording changes necessary for Web use. Whenever possible, variables, numbers, or words have been randomized so that each student receives a unique version of the question. This list is updated nightly.

##### Question Group Key
R - Review
TB - Test Bank
XP - Extra Problem

##### Question Availability Color Key
BLACK questions are available now
GRAY questions are under development

Group Quantity Questions
Chapter 1: Linear Equations and Vectors
1.R 48 001 002 003 004 005 006 007 008 011 012 013 015 017 018 019 020 021 022 023 024 025 026 027 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP 508.XP 509.XP 510.XP 511.XP 512.XP 513.XP 514.XP 515.XP 516.XP 517.XP 518.XP 519.XP 520.XP 521.XP 522.XP 523.XP 524.XP 525.XP
1.TB 28 001 002 003 004 005 006 007 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029
1.1 8 001 002 003 005 010 011 012 013
1.2 7 001 003 005 007 013 014 016
1.3 9 001 002 003 005 006 008 009 010 011
1.4 7 003 004 005 006 007 008 009
1.5 11 004 005 006 007 012 013 014 015 017 018 019
1.6 15 001 003 004 005 007 008 012 014 018 020 023 024 026 032 033
1.7 9 001 004 007 009 013 015 017 018 020
Chapter 2: Matrices and Linear Transformations
2.R 57 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 021 022 023 024 025 026 027 028 029 030 031 032 033 034 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP 508.XP 509.XP 510.XP 511.XP 512.XP 513.XP 514.XP 515.XP 516.XP 517.XP 518.XP 519.XP 520.XP 521.XP 522.XP 523.XP 524.XP 525.XP
2.TB 31 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031
2.1 7 001 003 005 008 010 014 016
2.2 7 004 005 007 024 025 044 045
2.3 6 001 003 015 021 022 024
2.4 12 001 002 003 005 006 008 009 011 013 015 018 040
2.5 6 002 005 006 011 022 024
2.6 7 007 009 013 018 021 023 026
2.7 3 001 003 006
2.8 5 001 004 006 012 014
2.9 5 002 004 009 013 028
Chapter 3: Determinants and Eigenvectors
3.R 50 001 002 003 004 005 006 007 008 009 010 011 012 013 014 016 018 019 020 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP 508.XP 509.XP 510.XP 511.XP 512.XP 513.XP 514.XP 515.XP 516.XP 517.XP 518.XP 519.XP 520.XP 521.XP 522.XP 523.XP 524.XP 525.XP 526.XP 527.XP 528.XP 529.XP 530.XP 531.XP 532.XP
3.TB 27 001 002 003 004 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028
3.1 14 001 002 003 004 005 006 007 008 009 010 011 013 015 019
3.2 9 001 002 003 004 008 009 012 013 014
3.3 10 001 003 005 006 008 010 013 014 016 017
3.4 9 003 005 007 011 012 014 016 018 035
3.5 10 001 002 004 005 006 007 008 010 011 012
Chapter 4: General Vector Spaces
4.R 122 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 035 036 037 038 039 040 041 042 043 044 045 046 047 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP 508.XP 509.XP 510.XP 511.XP 512.XP 513.XP 514.XP 515.XP 516.XP 517.XP 518.XP 519.XP 520.XP 521.XP 522.XP 523.XP 524.XP 525.XP 526.XP 527.XP 528.XP 529.XP 530.XP 531.XP 532.XP 533.XP 534.XP 535.XP 536.XP 537.XP 538.XP 539.XP 540.XP 541.XP 542.XP 543.XP 544.XP 545.XP 546.XP 547.XP 548.XP 549.XP 550.XP 551.XP 552.XP 553.XP 554.XP 555.XP 556.XP 557.XP 558.XP 559.XP 560.XP 561.XP 562.XP 563.XP 564.XP 565.XP 566.XP 567.XP 568.XP 569.XP 570.XP 571.XP 572.XP 573.XP 574.XP 575.XP
4.TB 34 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034
4.1 6 002 019 020 021 022 034
4.2 5 001 002 008 009 011
4.3 6 001 003 007 008 009 015
4.4 11 003 005 011 012 013 014 015 016 017 020 021
4.5 10 001 002 003 004 005 006 007 010 011 012
4.6 16 001 002 003 004 005 008 013 014 015 016 017 018 019 020 021 024
4.7 6 001 002 003 005 007 009
4.8 8 009 010 017 022 026 028 032 041
4.9 4 001 002 004 005
4.10 2 007 011
Chapter 5: Coordinate Representations
5.R 27 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP 508.XP 509.XP 510.XP
5.TB 32 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032
5.1 11 004 007 009 011 014 017 019 022 024 025 028
5.2 11 001 002 003 004 005 007 009 015 021 022 024
5.3 12 001 002 003 004 005 006 007 008 009 010 015 019
5.4 5 001 002 003 004 006
5.5 8 001 002 003 004 005 006 007 010
Chapter 6: Inner Product Spaces
6.R 18 001 002 003 004 005 006 007 008 009 010 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP 508.XP
6.TB 26 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026
6.1 12 008 009 012 013 014 015 016 017 019 020 021.alt 022.alt
6.2 8 001 004 007 009 010 011 012 013
6.3 13 001 002 003 004 005 006 007 008 009 010 011 012 015
6.4 29 001 002 003 004 005 007 008 010 012 013 014 016 018 020 021 022 023 024 025 026 027 028 029 030 031 032 033 034 037
Chapter 7: Numerical Methods
7.R 19 001 002 003 004 005 006 007 008 009 010 011 012 501.XP 502.XP 503.XP 504.XP 505.XP 506.XP 507.XP
7.TB 28 001 002 003 004 005 006 007 008 009 010 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029
7.1 9 001 002 003 004 005 006 007 009 011
7.2 22 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 026
7.3 12 001 002 003 005 006 011 012 013 014 015 016 017
7.4 7 001 002 003 004 005 006 007
7.5 14 001 002 003 004 005 006 007 008 009 010 011 012 013 015
7.6 35 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025 026 027 028 029 030 031 032 035 043 044
Chapter 8: Linear Programming
8.R 8 001 002 003 004 005 006 007 008
8.TB 15 001 002 003 004 007 009 010 011 012 013 014 015 016 017 018
8.1 20 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016 017 018 019 020
8.2 16 001 002 003 004 005 006 007 008 009 010 011 012 013 014 015 016
8.3 6 001 002 003 004 005 006
Total 1070