1. Vectors, Lines, and Planes

4hr

1.1.1. Basics of Vectors5 min

1.1.2. Example1 min

1.1.3. Example1 min

1.1.4. Practice2 min

1.2.1. Vector Operations8 min

1.2.7. Practice (Tricky)5 min

1.3.1. Vector Properties4 min

1.3.2. Example3 min

1.3.3. Example3 min

1.3.4. Practice: Vector Properties2 min

1.4.1. Vector Norm5 min

1.5.1. Unit Vectors5 min

1.5.2. Example2 min

1.5.3. Practice2 min

1.6.1. Basics of Dot Product2 min

1.6.2. Example2 min

1.6.3. Practice1 min

1.7.1. Dot Product Properties3 min

1.8.1. Angle Between Vectors3 min

1.8.2. Example2 min

1.8.3. Example2 min

1.8.4. Practice: Dot Product & Angle2 min

1.8.5. Practice2 min

1.8.6. Practice

1.9.1. Projection and Perpendicular3 min

1.9.6. Practice: Projections

1.10.1. Cross Product4 min

1.10.2. Example3 min

1.10.3. Practice2 min

1.11.1. Cross Product Properties4 min

1.11.2. Example2 min

1.11.3. Example2 min

1.11.4. Practice2 min

1.11.5. Practice2 min

1.12.1. Cross Product and Area2 min

1.12.2. Example3 min

1.12.3. Practice4 min

1.13.1. Volume of a Parallelepiped1 min

1.13.2. Example2 min

1.13.3. Practice1 min

1.14.1. Lines in

\reals^n

8 min

1.14.2. Example3 min

1.14.3. Example3 min

1.14.4. Practice2 min

1.14.5. Practice

1.14.6. Practice

1.15.1. Equations of Planes in

\reals^3

5 min

1.15.2. Example2 min

1.15.3. Example4 min

1.15.4. Practice2 min

1.15.5. Practice

1.15.6. Practice (Tricky)4 min

1.16.1. Hyperplanes3 min

1.16.2. Example1 min

1.16.3. Practice3 min

1.17.1. Distances5 min

1.17.2. Example3 min

1.17.3. Example3 min

1.17.4. Practice4 min

1.17.5. Practice3 min

1.18.1. Intersection of Two Lines3 min

1.18.2. Example2 min

1.18.3. Example3 min

1.18.4. Example2 min

1.18.5. Practice2 min

1.18.6. Practice7 min

1.19.1. Intersection of Lines and Planes2 min

1.19.2. Example2 min

1.19.3. Example3 min

1.19.4. Practice1 min

1.19.5. Practice1 min

2. Intro to Linear Systems

1.6hr

2.1.1. Basics of Systems of Linear Equations8 min

2.1.2. Example3 min

2.1.3. Practice2 min

2.1.4. Practice3 min

2.2.1. Augmented Matrix3 min

2.3.1. Echelon Forms5 min

2.4.1. Reducing a Matrix5 min

2.5.1. Rank of a Matrix5 min

2.5.2. Example3 min

2.5.3. Practice38 sec

2.5.4. Practice1 min

2.6.1. Solving Linear Systems5 min

2.6.2. Homogeneous Systems2 min

2.7.1. Geometric Interpretation of Solutions to SLEs4 min

2.7.2. Example3 min

2.7.3. Practice3 min

3. Linear Transformations and Matrix Algebra

2.3hr

3.1.1. Basics of Matrices3 min

3.1.2. Matrix Arithmetic3 min

3.1.3. Example1 min

3.1.4. Practice2 min

3.2.1. Matrix Multiplication6 min

3.3.1. Matrix Transpose3 min

3.3.2. Symmetric Matrices3 min

3.3.3. Example3 min

3.3.4. Practice60 sec

3.3.5. Practice2 min

3.4.1. Linear Transformations6 min

3.5.1. Special Linear Transformations in

\reals^2

3.6.1. Composition and Inverse3 min

3.6.2. Example4 min

3.6.3. Practice3 min

3.7.1. Matrix Inverse4 min

3.7.2. Example3 min

3.7.3. Practice32 sec

3.7.4. Practice2 min

3.8.1. Matrix Inverse Algorithm3 min

3.8.2. Example2 min

3.8.3. Example2 min

3.8.4. Practice2 min

3.9.1. Elementary Matrices7 min

3.10.1. Invertible Matrix Theorem2 min

3.10.2. Example1 min

3.10.3. Practice1 min

3.11.1. Solving Matrix Equations2 min

3.11.2. Example52 sec

3.11.3. Example4 min

3.11.4. Practice2 min

3.11.5. Practice54 sec

3.11.6. Practice2 min

4. Determinants

58min

5. Subspaces, Independence, and Coordinates

1.3hr

6. Orthogonality

21min

6.1.1. Orthonormal Set3 min

6.1.2. Example2 min

6.1.3. Gram-Schmidt Process3 min

6.1.4. Example4 min

6.1.5. Practice

6.2.1. Least Squares Approximation6 min

6.2.2. Example4 min

6.2.3. Example: Least Squares for Polynomials

6.2.4. Practice

7. Eigenvalues and Eigenvectors (Spectral Theory)

1.7hr

8. Appendix: Complex Numbers

1.1hr

8.1.1. Basics of Complex Numbers4 min

8.1.2. Operations With Complex Numbers9 min

8.1.3. Example5 min

8.1.4. Practice3 min

8.2.1. Polar Form7 min

8.2.2. Geometric Interpretation of Multiplication4 min

8.2.3. Example8 min

8.2.4. Practice1 min

8.2.5. Practice4 min

8.3.1. Powers and Root6 min

MAT188H1

Course Overview

Grade Boosters

1. Vectors, Lines, and Planes

2. Intro to Linear Systems

3. Linear Transformations and Matrix Algebra

4. Determinants

5. Subspaces, Independence, and Coordinates

6. Orthogonality

7. Eigenvalues and Eigenvectors (Spectral Theory)

8. Appendix: Complex Numbers

Midterm 2 Overview

Course Notes