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Linear Algebra for Team-Based Inquiry Learning:
2023 Edition
Steven Clontz, Drew Lewis
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Front Matter
Colophon
TBIL Resource Library
For Instructors
Video Resources
Slideshows
1
Systems of Linear Equations (LE)
1.1
Linear Systems, Vector Equations, and Augmented Matrices (LE1)
1.1.1
Class Activities
1.1.2
Videos
1.1.3
Slideshow
1.1.4
Exercises
1.1.5
Mathematical Writing Explorations
1.1.6
Sample Problem and Solution
1.2
Row Reduction of Matrices (LE2)
1.2.1
Class Activities
1.2.2
Videos
1.2.3
Slideshow
1.2.4
Exercises
1.2.5
Mathematical Writing Explorations
1.2.6
Sample Problem and Solution
1.3
Counting Solutions for Linear Systems (LE3)
1.3.1
Class Activities
1.3.2
Videos
1.3.3
Slideshow
1.3.4
Exercises
1.3.5
Mathematical Writing Explorations
1.3.6
Sample Problem and Solution
1.4
Linear Systems with Infinitely-Many Solutions (LE4)
1.4.1
Class Activities
1.4.2
Videos
1.4.3
Slideshow
1.4.4
Exercises
1.4.5
Mathematical Writing Explorations
1.4.6
Sample Problem and Solution
2
Euclidean Vectors (EV)
2.1
Linear Combinations (EV1)
2.1.1
Class Activities
2.1.2
Videos
2.1.3
Slideshow
2.1.4
Exercises
2.1.5
Mathematical Writing Explorations
2.1.6
Sample Problem and Solution
2.2
Spanning Sets (EV2)
2.2.1
Class Activities
2.2.2
Videos
2.2.3
Slideshow
2.2.4
Exercises
2.2.5
Mathematical Writing Explorations
2.2.6
Sample Problem and Solution
2.3
Subspaces (EV3)
2.3.1
Class Activities
2.3.2
Videos
2.3.3
Slideshow
2.3.4
Exercises
2.3.5
Mathematical Writing Explorations
2.3.6
Sample Problem and Solution
2.4
Linear Independence (EV4)
2.4.1
Class Activities
2.4.2
Videos
2.4.3
Slideshow
2.4.4
Exercises
2.4.5
Mathematical Writing Explorations
2.4.6
Sample Problem and Solution
2.5
Identifying a Basis (EV5)
2.5.1
Class Activities
2.5.2
Videos
2.5.3
Slideshow
2.5.4
Exercises
2.5.5
Mathematical Writing Explorations
2.5.6
Sample Problem and Solution
2.6
Subspace Basis and Dimension (EV6)
2.6.1
Class Activities
2.6.2
Videos
2.6.3
Slideshow
2.6.4
Exercises
2.6.5
Mathematical Writing Explorations
2.6.6
Sample Problem and Solution
2.7
Homogeneous Linear Systems (EV7)
2.7.1
Class Activities
2.7.2
Videos
2.7.3
Slideshow
2.7.4
Exercises
2.7.5
Mathematical Writing Explorations
2.7.6
Sample Problem and Solution
3
Algebraic Properties of Linear Maps (AT)
3.1
Linear Transformations (AT1)
3.1.1
Class Activities
3.1.2
Videos
3.1.3
Slideshow
3.1.4
Exercises
3.1.5
Mathematical Writing Explorations
3.1.6
Sample Problem and Solution
3.2
Standard Matrices (AT2)
3.2.1
Class Activities
3.2.2
Videos
3.2.3
Slideshow
3.2.4
Exercises
3.2.5
Mathematical Writing Explorations
3.2.6
Sample Problem and Solution
3.3
Image and Kernel (AT3)
3.3.1
Class Activities
3.3.2
Videos
3.3.3
Slideshow
3.3.4
Exercises
3.3.5
Mathematical Writing Explorations
3.3.6
Sample Problem and Solution
3.4
Injective and Surjective Linear Maps (AT4)
3.4.1
Class Activities
3.4.2
Videos
3.4.3
Slideshow
3.4.4
Exercises
3.4.5
Mathematical Writing Explorations
3.4.6
Sample Problem and Solution
3.5
Vector Spaces (AT5)
3.5.1
Class Activities
3.5.2
Videos
3.5.3
Slideshow
3.5.4
Exercises
3.5.5
Mathematical Writing Explorations
3.5.6
Sample Problem and Solution
3.6
Polynomial and Matrix Spaces (AT6)
3.6.1
Class Activities
3.6.2
Videos
3.6.3
Slideshow
3.6.4
Exercises
3.6.5
Mathematical Writing Explorations
3.6.6
Sample Problem and Solution
4
Matrices (MX)
4.1
Matrices and Multiplication (MX1)
4.1.1
Class Activities
4.1.2
Videos
4.1.3
Slideshow
4.1.4
Exercises
4.1.5
Mathematical Writing Explorations
4.1.6
Sample Problem and Solution
4.2
The Inverse of a Matrix (MX2)
4.2.1
Class Activities
4.2.2
Videos
4.2.3
Slideshow
4.2.4
Exercises
4.2.5
Mathematical Writing Explorations
4.2.6
Sample Problem and Solution
4.3
Solving Systems with Matrix Inverses (MX3)
4.3.1
Class Activities
4.3.2
Videos
4.3.3
Exercises
4.3.4
Mathematical Writing Explorations
4.3.5
Sample Problem and Solution
4.4
Row Operations as Matrix Multiplication (MX4)
4.4.1
Class Activities
4.4.2
Videos
4.4.3
Slideshow
4.4.4
Exercises
4.4.5
Sample Problem and Solution
5
Geometric Properties of Linear Maps (GT)
5.1
Row Operations and Determinants (GT1)
5.1.1
Class Activities
5.1.2
Videos
5.1.3
Slideshow
5.1.4
Exercises
5.1.5
Mathematical Writing Explorations
5.1.6
Sample Problem and Solution
5.2
Computing Determinants (GT2)
5.2.1
Class Activities
5.2.2
Videos
5.2.3
Slideshow
5.2.4
Exercises
5.2.5
Mathematical Writing Explorations
5.2.6
Sample Problem and Solution
5.3
Eigenvalues and Characteristic Polynomials (GT3)
5.3.1
Class Activities
5.3.2
Videos
5.3.3
Slideshow
5.3.4
Exercises
5.3.5
Mathematical Writing Explorations
5.3.6
Sample Problem and Solution
5.4
Eigenvectors and Eigenspaces (GT4)
5.4.1
Class Activities
5.4.2
Videos
5.4.3
Slideshow
5.4.4
Exercises
5.4.5
Mathematical Writing Explorations
5.4.6
Sample Problem and Solution
Back Matter
A
Applications
A.1
Civil Engineering: Trusses and Struts
A.1.1
Activities
A.1.2
Slideshow
A.2
Computer Science: PageRank
A.2.1
Activities
A.2.2
Slideshow
A.3
Geology: Phases and Components
A.3.1
Activities
A.3.2
Slideshow
B
Appendix
B.1
Sample Exercises with Solutions
B.2
Definitions
Index
🔗
Section
B.2
Definitions
1.1
Linear Systems, Vector Equations, and Augmented Matrices (LE1)
Definition 1.1.1
Definition 1.1.3
Definition 1.1.6
Definition 1.1.13
1.2
Row Reduction of Matrices (LE2)
Definition 1.2.1
Definition 1.2.3
Definition 1.2.6
1.4
Linear Systems with Infinitely-Many Solutions (LE4)
Definition 1.4.2
2.1
Linear Combinations (EV1)
Definition 2.1.2
Definition 2.1.3
2.3
Subspaces (EV3)
Definition 2.3.1
2.4
Linear Independence (EV4)
Definition 2.4.2
2.5
Identifying a Basis (EV5)
Definition 2.5.3
Definition 2.5.7
2.6
Subspace Basis and Dimension (EV6)
Definition 2.6.3
Definition 2.6.8
2.7
Homogeneous Linear Systems (EV7)
Definition 2.7.1
3.1
Linear Transformations (AT1)
Definition 3.1.1
Definition 3.1.2
3.2
Standard Matrices (AT2)
Definition 3.2.7
3.3
Image and Kernel (AT3)
Definition 3.3.2
Definition 3.3.7
3.4
Injective and Surjective Linear Maps (AT4)
Definition 3.4.1
Definition 3.4.4
Definition 3.4.11
3.5
Vector Spaces (AT5)
Definition 3.5.6
4.1
Matrices and Multiplication (MX1)
Definition 4.1.3
4.2
The Inverse of a Matrix (MX2)
Definition 4.2.2
Definition 4.2.6
5.1
Row Operations and Determinants (GT1)
Definition 5.1.13
5.3
Eigenvalues and Characteristic Polynomials (GT3)
Definition 5.3.4
Definition 5.3.7
5.4
Eigenvectors and Eigenspaces (GT4)
Definition 5.4.2
A.1
Civil Engineering: Trusses and Struts
Definition A.1.1
A.3
Geology: Phases and Components
Definition A.3.1
