Diablo Valley College Application of Linear Algebra in Engineering Paper you may cite the text (see end of each chapter) for applications or you may cite o

Diablo Valley College Application of Linear Algebra in Engineering Paper you may cite the text (see end of each chapter) for applications or you may cite other textbooks. The report must be 3 typed pages (12 inch font), double spaced, and it must include a Bibliography. You must have three sources , two of which must be book sources. Index of Applications
BIOLOGY AND LIFE SCIENCES
Age distribution vector, 378, 391, 392, 395
Age progression software, 180
Age transition matrix, 378, 391, 392, 395
Agriculture, 37, 50
Cosmetic surgery results simulation, 180
Duchenne muscular dystrophy, 365
Galloping speeds of animals, 276
Genetics, 365
Health care expenditures, 146
Heart rhythm analysis, 255
Hemophilia A, 365
Hereditary baldness, 365
Nutrition, 11
Population
of deer, 37
of laboratory mice, 91
of rabbits, 379
of sharks, 396
of small fish, 396
Population age and growth over time, 331
Population genetics, 365
Population growth, 378, 379, 391, 392,
395, 396, 398
Predator-prey relationship, 396
Red-green color blindness, 365
Reproduction rates of deer, 103
Sex-linked inheritance, 365
Spread of a virus, 91, 93
Vitamin C content, 11
Wound healing simulation, 180
X-linked inheritance, 365
BUSINESS AND ECONOMICS
Airplane allocation, 91
Borrowing money, 23
Demand, for a rechargeable power drill, 103
Demand matrix, external, 98
Economic system, 97, 98
of a small community, 103
Finance, 23
Fundraising, 92
Gasoline sales, 105
Industrial system, 102, 107
Input-output matrix, 97
Leontief input-output model(s), 97, 98, 103
Major League Baseball salaries, 107
Manufacturing
labor and material costs, 105
models and prices, 150
production levels, 51, 105
Net profit, Microsoft, 32
Output matrix, 98
Petroleum production, 292
Profit, from crops, 50
Purchase of a product, 91
Revenue
fast-food stand, 242
General Dynamics Corporation, 266, 276
Google, Inc., 291
telecommunications company, 242
software publishers, 143
Sales, 37
concession area, 42
stocks, 92
Wal-Mart, 32
Sales promotion, 106
Satellite television service, 85, 86, 147
Software publishing, 143
ENGINEERING AND TECHNOLOGY
Aircraft design, 79
Circuit design, 322
Computer graphics, 338
Computer monitors, 190
Control system, 314
Controllability matrix, 314
Cryptography, 94–96, 102, 107
Data encryption, 94
Decoding a message, 96, 102, 107
Digital signal processing, 172
Electrical network analysis, 30, 31, 34, 37,
150
Electronic equipment, 190
Encoding a message, 95, 102, 107
Encryption key, 94
Engineering and control, 130
Error checking
digit, 200
matrix, 200
Feed horn, 223
Global Positioning System, 16
Google’s Page Rank algorithm, 86
Image morphing and warping, 180
Information retrieval, 58
Internet search engine, 58
Ladder network, 322
Locating lost vessels at sea, 16
Movie special effects, 180
Network analysis, 29–34, 37
Radar, 172
Sampling, 172
Satellite dish, 223
Smart phones, 190
Televisions, 190
Wireless communications, 172
MATHEMATICS AND GEOMETRY
Adjoint of a matrix, 134, 135, 142, 146, 150
Collinear points in the xy-plane, 139, 143
Conic section(s), 226, 229
general equation, 141
rotation of axes, 221–224, 226, 229,
   383–385, 392, 395
Constrained optimization, 389, 390, 392,
  395
Contraction in R2, 337, 341, 342
Coplanar points in space, 140, 143
Cramer’s Rule, 130, 136, 137, 142, 143, 146
Cross product of two vectors, 277–280,
288, 289, 294
Differential equation(s)
linear, 218, 225, 226, 229
second order, 164
system of first order, 354, 380, 381,
   391, 392, 395, 396, 398
Expansion in R2, 337, 341, 342, 345
Fibonacci sequence, 396
Fourier approximation(s), 285–287, 289, 292
Geometry of linear transformations in R2,
336–338, 341, 342, 345
Hessian matrix, 375
Jacobian, 145
Lagrange multiplier, 34
Laplace transform, 130
Least squares approximation(s), 281–284, 289
linear, 282, 289, 292
quadratic, 283, 289, 292
Linear programming, 47
Magnification in R2, 341, 342
Mathematical modeling, 273, 274, 276
Parabola passing through three points, 150
Partial fraction decomposition, 34, 37
Polynomial curve fitting, 25–28, 32, 34, 37
Quadratic form(s), 382–388, 392, 395, 398
Quadric surface, rotation of, 388, 392
Reflection in R2, 336, 341, 342, 345, 346
Relative maxima and minima, 375
Rotation
in R2, 303, 343, 393, 397
in R3, 339, 340, 342, 345
Second Partials Test for relative extrema, 375
Shear in R2, 337, 338, 341, 342, 345
Taylor polynomial of degree 1, 282
Three-point form of the equation of a plane,
141, 143, 146
Translation in R2, 308, 343
Triple scalar product, 288
Two-point form of the equation of a line,
139, 143, 146, 150
Unit circle, 253
Wronskian, 219, 225, 226, 229
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PHYSICAL SCIENCES
Acoustical noise levels, 28
Airplane speed, 11
Area
of a parallelogram using cross product,
   279, 280, 288, 294
of a triangle
using cross product, 289
using determinants, 138, 142, 146,
  150
Astronomy, 27, 274
Balancing a chemical equation, 4
Beam deflection, 64, 72
Chemical
changing state, 91
mixture, 37
reaction, 4
Comet landing, 141
Computational fluid dynamics, 79
Crystallography, 213
Degree of freedom, 164
Diffusion, 354
Dynamical systems, 396
Earthquake monitoring, 16
Electric and magnetic flux, 240
Flexibility matrix, 64, 72
Force
matrix, 72
to pull an object up a ramp, 157
Geophysics, 172
Grayscale, 190
Hooke’s Law, 64
Kepler’s First Law of Planetary Motion, 141
Kirchhoff’s Laws, 30, 322
Lattice of a crystal, 213
Mass-spring system, 164, 167
Mean distance from the sun, 27, 274
Natural frequency, 164
Newton’s Second Law of Motion, 164
Ohm’s Law, 322
Pendulum, 225
Planetary periods, 27, 274
Primary additive colors, 190
RGB color model, 190
Stiffness matrix, 64, 72
Temperature, 34
Torque, 277
Traffic flow, 28, 33
Undamped system, 164
Unit cell, 213
end-centered monoclinic, 213
Vertical motion, 37
Volume
of a parallelepiped, 288, 289, 292
of a tetrahedron, 114, 140, 143
Water flow, 33
Wind energy consumption, 103
Work, 248
SOCIAL SCIENCES AND
DEMOGRAPHICS
Caribbean Cruise, 106
Cellular phone subscribers, 107
Consumer preference model, 85, 86, 92, 147
Final grades, 105
Grade distribution, 92
Master’s degrees awarded, 276
Politics, voting apportionment, 51
Population
of consumers, 91
regions of the United States, 51
of smokers and nonsmokers, 91
United States, 32
world, 273
Population migration, 106
Smokers and nonsmokers, 91
Sports
activities, 91
Super Bowl I, 36
Television watching, 91
Test scores, 108
STATISTICS AND PROBABILITY
Canonical regression analysis, 304
Least squares regression
analysis, 99–101, 103, 107, 265, 271–276
cubic polynomial, 276
line, 100, 103, 107, 271, 274, 276, 296
quadratic polynomial, 273, 276
Leslie matrix, 331, 378
Markov chain, 85, 86, 92, 93, 106
absorbing, 89, 90, 92, 93, 106
Multiple regression analysis, 304
Multivariate statistics, 304
State matrix, 85, 106, 147, 331
Steady state probability vector, 386
Stochastic matrices, 84–86, 91–93, 106, 331
MISCELLANEOUS
Architecture, 388
Catedral Metropolitana Nossa Senhora
Aparecida, 388
Chess tournament, 93
Classified documents, 106
Determining directions, 16
Dominoes, A2
Flight crew scheduling, 47
Sudoku, 120
Tips, 23
U.S. Postal Service, 200
ZIP + 4 barcode, 200
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Elementary Linear Algebra
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Elementary Linear Algebra
8e
Ron Larson
The Pennsylvania State University
The Behrend College
Australia • Brazil • Mexico • Singapore • United Kingdom • United States
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Elementary Linear Algebra
Eighth Edition
Ron Larson
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Contents
1
Systems of Linear Equations
1.1
1.2
1.3
2
3
2
13
25
35
38
38
Matrices
39
2.1
2.2
2.3
2.4
2.5
2.6
40
52
62
74
84
94
104
108
108
Operations with Matrices
Properties of Matrix Operations
The Inverse of a Matrix
Elementary Matrices
Markov Chains
More Applications of Matrix Operations
Review Exercises
Project 1 Exploring Matrix Multiplication
Project 2 Nilpotent Matrices
Determinants
3.1
3.2
3.3
3.4
4
Introduction to Systems of Linear Equations
Gaussian Elimination and Gauss-Jordan Elimination
Applications of Systems of Linear Equations
Review Exercises
Project 1 Graphing Linear Equations
Project 2 Underdetermined and Overdetermined Systems
1
The Determinant of a Matrix
Determinants and Elementary Operations
Properties of Determinants
Applications of Determinants
Review Exercises
Project 1 Stochastic Matrices
Project 2 The Cayley-Hamilton Theorem
Cumulative Test for Chapters 1–3
Vector Spaces
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
Rn
Vectors in
Vector Spaces
Subspaces of Vector Spaces
Spanning Sets and Linear Independence
Basis and Dimension
Rank of a Matrix and Systems of Linear Equations
Coordinates and Change of Basis
Applications of Vector Spaces
Review Exercises
Project 1 Solutions of Linear Systems
Project 2 Direct Sum
109
110
118
126
134
144
147
147
149
151
152
161
168
175
186
195
208
218
227
230
230
v
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vi
Contents
5
Inner Product Spaces
5.1
5.2
5.3
5.4
5.5
6
Linear Transformations
6.1
6.2
6.3
6.4
6.5
7
Introduction to Linear Transformations
The Kernel and Range of a Linear Transformation
Matrices for Linear Transformations
Transition Matrices and Similarity
Applications of Linear Transformations
Review Exercises
Project 1 Reflections in R 2 (I)
Project 2 Reflections in R 2 (II)
Eigenvalues and Eigenvectors
7.1
7.2
7.3
7.4
8
Length and Dot Product in R n
Inner Product Spaces
Orthonormal Bases: Gram-Schmidt Process
Mathematical Models and Least Squares Analysis
Applications of Inner Product Spaces
Review Exercises
Project 1 The QR-Factorization
Project 2 Orthogonal Matrices and Change of Basis
Cumulative Test for Chapters 4 and 5
Eigenvalues and Eigenvectors
Diagonalization
Symmetric Matrices and Orthogonal Diagonalization
Applications of Eigenvalues and Eigenvectors
Review Exercises
Project 1 Population Growth and Dynamical Systems (I)
Project 2 The Fibonacci Sequence
Cumulative Test for Chapters 6 and 7
231
232
243
254
265
277
290
293
294
295
297
298
309
320
330
336
343
346
346
347
348
359
368
378
393
396
396
397
Complex Vector Spaces (online)*
8.1
8.2
8.3
8.4
8.5
Complex Numbers
Conjugates and Division of Complex Numbers
Polar Form and DeMoivre’s Theorem
Complex Vector Spaces and Inner Products
Unitary and Hermitian Matrices
Review Exercises
Project 1 The Mandelbrot Set
Project 2 Population Growth and Dynamical Systems (II)
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Contents
9
Linear Programming (online)*
9.1
9.2
9.3
9.4
9.5
10
vii
Systems of Linear Inequalities
Linear Programming Involving Two Variables
The Simplex Method: Maximization
The Simplex Method: Minimization
The Simplex Method: Mixed Constraints
Review Exercises
Project 1 Beach Sand Replenishment (I)
Project 2 Beach Sand Replenishment (II)
Numerical Methods (online)*
10.1
10.2
10.3
10.4
Gaussian Elimination with Partial Pivoting
Iterative Methods for Solving Linear Systems
Power Method for Approximating Eigenvalues
Applications of Numerical Methods
Review Exercises
Project 1 The Successive Over-Relaxation (SOR) Method
Project 2 United States Population
Appendix
A1
Mathematical Induction and Other Forms of Proofs
Answers to Odd-Numbered Exercises and Tests
Index
Technology Guide*
*Available online at CengageBrain.com.
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A7
A41
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Preface
Welcome to Elementary Linear Algebra, Eighth Edition. I am proud to present to you this new edition. As with
all editions, I have been able to incorporate many useful comments from you, our user. And while much has
changed in this revision, you will still find what you expect—a pedagogically sound, mathematically precise, and
comprehensive textbook. Additionally, I am pleased and excited to offer you something brand new— a companion
website at LarsonLinearAlgebra.com. My goal for every edition of this textbook is to provide students with the
tools that they need to master linear algebra. I hope you find that the changes in this edition, together with
LarsonLinearAlgebra.com, will help accomplish just that.
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