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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
TBIL Resource Library
For Instructors
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 Activities
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
🔗
Appendix
A
Applications
A.1
Civil Engineering: Trusses and Struts
A.2
Computer Science: PageRank
A.3
Geology: Phases and Components
