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Linear Algebra for Team-Based Inquiry Learning:
PREVIEW Edition — Instructor Version
Steven Clontz, Drew Lewis
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Front Matter
Colophon
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Video Resources
1
Systems of Linear Equations (LE)
1.1
Linear Systems, Vector Equations, and Augmented Matrices (LE1)
1.1.1
Warm Up
1.1.2
Class Activities
1.1.3
Individual Practice
1.1.4
Videos
1.1.5
Exercises
1.1.6
Mathematical Writing Explorations
1.1.7
Sample Problem and Solution
1.2
Row Reduction of Matrices (LE2)
1.2.1
Warm Up
1.2.2
Class Activities
1.2.3
Individual Practice
1.2.4
Videos
1.2.5
Exercises
1.2.6
Mathematical Writing Explorations
1.2.7
Sample Problem and Solution
1.3
Counting Solutions for Linear Systems (LE3)
1.3.1
Warm Up
1.3.2
Class Activities
1.3.3
Individual Practice
1.3.4
Videos
1.3.5
Exercises
1.3.6
Mathematical Writing Explorations
1.3.7
Sample Problem and Solution
1.4
Linear Systems with Infinitely-Many Solutions (LE4)
1.4.1
Warm Up
1.4.2
Class Activities
1.4.3
Individual Practice
1.4.4
Videos
1.4.5
Exercises
1.4.6
Mathematical Writing Explorations
1.4.7
Sample Problem and Solution
2
Euclidean Vectors (EV)
2.1
Linear Combinations (EV1)
2.1.1
Warm Up
2.1.2
Class Activities
2.1.3
Individual Practice
2.1.4
Videos
2.1.5
Exercises
2.1.6
Mathematical Writing Explorations
2.1.7
Sample Problem and Solution
2.2
Spanning Sets (EV2)
2.2.1
Warm Up
2.2.2
Class Activities
2.2.3
Individual Practice
2.2.4
Videos
2.2.5
Exercises
2.2.6
Mathematical Writing Explorations
2.2.7
Sample Problem and Solution
2.3
Subspaces (EV3)
2.3.1
Warm Up
2.3.2
Class Activities
2.3.3
Individual Practice
2.3.4
Videos
2.3.5
Exercises
2.3.6
Mathematical Writing Explorations
2.3.7
Sample Problem and Solution
2.4
Linear Independence (EV4)
2.4.1
Warm Up
2.4.2
Class Activities
2.4.3
Individual Practice
2.4.4
Videos
2.4.5
Exercises
2.4.6
Mathematical Writing Explorations
2.4.7
Sample Problem and Solution
2.5
Identifying a Basis (EV5)
2.5.1
Warm Up
2.5.2
Class ActivitiesInstructor Note
2.5.3
Individual Practice
2.5.4
Videos
2.5.5
Exercises
2.5.6
Mathematical Writing Explorations
2.5.7
Sample Problem and Solution
2.6
Subspace Basis and Dimension (EV6)
2.6.1
Warm Up
2.6.2
Class Activities
2.6.3
Individual Practice
2.6.4
Videos
2.6.5
Exercises
2.6.6
Mathematical Writing Explorations
2.6.7
Sample Problem and Solution
2.7
Homogeneous Linear Systems (EV7)
2.7.1
Warmup
2.7.2
Class Activities
2.7.3
Individual Practice
2.7.4
Videos
2.7.5
Exercises
2.7.6
Mathematical Writing Explorations
2.7.7
Sample Problem and Solution
3
Algebraic Properties of Linear Maps (AT)
3.1
Linear Transformations (AT1)
3.1.1
Warm Up
3.1.2
Class Activities
3.1.3
Individual Practice
3.1.4
Videos
3.1.5
Exercises
3.1.6
Mathematical Writing Explorations
3.1.7
Sample Problem and Solution
3.2
Standard Matrices (AT2)
3.2.1
Warm Up
3.2.2
Class Activities
3.2.3
Individual Practice
3.2.4
Videos
3.2.5
Exercises
3.2.6
Mathematical Writing Explorations
3.2.7
Sample Problem and Solution
3.3
Image and Kernel (AT3)
3.3.1
Warm Up
3.3.2
Class Activities
3.3.3
Individual Practice
3.3.4
Videos
3.3.5
Exercises
3.3.6
Mathematical Writing Explorations
3.3.7
Sample Problem and Solution
3.4
Injective and Surjective Linear Maps (AT4)
3.4.1
Warm Up
3.4.2
Class Activities
3.4.1
Individual Practice
3.4.3
Videos
3.4.5
Exercises
3.4.5
Mathematical Writing Explorations
3.4.6
Sample Problem and Solution
3.5
Vector Spaces (AT5)
3.5.1
Warm Up
3.5.2
Class Activities
3.5.3
Cooldown
3.5.4
Videos
3.5.5
Exercises
3.5.6
Mathematical Writing Explorations
3.5.7
Sample Problem and Solution
3.6
Polynomial and Matrix Spaces (AT6)
3.6.1
Warm Up
3.6.2
Class Activities
3.6.3
Individual Practice
3.6.4
Videos
3.6.5
Exercises
3.6.6
Mathematical Writing Explorations
3.6.7
Sample Problem and Solution
4
Matrices (MX)
4.1
Matrices and Multiplication (MX1)
4.1.1
Warm Up
4.1.2
Class Activities
4.1.3
Individual Practice
4.1.4
Videos
4.1.5
Exercises
4.1.6
Mathematical Writing Explorations
4.1.7
Sample Problem and Solution
4.2
The Inverse of a Matrix (MX2)
4.2.1
Warm Up
4.2.2
Class Activities
4.2.3
Individual Practice
4.2.4
Videos
4.2.5
Exercises
4.2.6
Mathematical Writing Explorations
4.2.7
Sample Problem and Solution
4.3
Solving Systems with Matrix Inverses (MX3)
4.3.1
Warm Up
4.3.2
Class Activities
4.3.3
Individual Practice
4.3.4
Videos
4.3.5
Exercises
4.3.6
Mathematical Writing Explorations
4.3.7
Sample Problem and Solution
4.4
Row Operations as Matrix Multiplication (MX4)
4.4.1
Warm Up
4.4.2
Class Activities
4.4.3
Individual Practice
4.4.4
Videos
4.4.5
Exercises
4.4.6
Sample Problem and Solution
5
Geometric Properties of Linear Maps (GT)
5.1
Row Operations and Determinants (GT1)
5.1.1
Warm Up
5.1.2
Class Activities
5.1.3
Individual Practice
5.1.4
Videos
5.1.5
Exercises
5.1.6
Mathematical Writing Explorations
5.1.7
Sample Problem and Solution
5.2
Computing Determinants (GT2)
5.2.1
Warm Up
5.2.2
Class Activities
5.2.3
Individual Practice
5.2.4
Videos
5.2.5
Exercises
5.2.6
Mathematical Writing Explorations
5.2.7
Sample Problem and Solution
5.3
Eigenvalues and Characteristic Polynomials (GT3)
5.3.1
Warm Up
5.3.2
Class Activities
5.3.3
Individual Practice
5.3.4
Videos
5.3.5
Exercises
5.3.6
Mathematical Writing Explorations
5.3.7
Sample Problem and Solution
5.4
Eigenvectors and Eigenspaces (GT4)
5.4.1
Warm Up
5.4.2
Class Activities
5.4.3
Individual Practice
5.4.4
Videos
5.4.5
Exercises
5.4.6
Mathematical Writing Explorations
5.4.7
Sample Problem and Solution
Back Matter
A
Applications
A.1
Civil Engineering: Trusses and Struts
A.1.1
Activities
A.2
Computer Science: PageRank
A.2.1
Activities
A.3
Geology: Phases and Components
A.3.1
Activities
B
Appendix
B.1
Sample Exercises with Solutions
B.2
Definitions
Index
🔗
Linear Algebra for Team-Based Inquiry Learning:
PREVIEW Edition — Instructor Version
Steven Clontz
Department of Mathematics and Statistics
University of South Alabama
sclontz@southalabama.edu
Drew Lewis
drew.lewis@gmail.com
Contributing Authors
Jessalyn Bolkema
Department of Mathematics
California State University, Dominguez Hills
jbolkema@csudh.edu
Jeff Ford
Department of Mathematics, Computer Science, and Statistics
Gustavus Adolphus College
jford@gustavus.edu
Jordan Kostiuk
Department of Mathematics
Brown University
jordan_kostiuk@brown.edu
Sharona Krinsky
Department of Mathematics
California State University, Los Angeles
skrinsk@calstatela.edu
Jennifer Nordstrom
Department of Mathematics
Linfield University
jnordstrom@linfield.edu
Kate Owens
Department of Mathematics
College of Charleston
owensks@cofc.edu
December 17, 2024
Colophon
TBIL Resource Library
For Instructors
Video Resources
