1. Algebra and Geometry (Chapters 1-3)

4hr

1.1.1. Basics of Complex Numbers4 min

1.1.2. Operations With Complex Numbers9 min

1.1.3. Example5 min

1.1.4. Practice3 min

1.1.5. Polar Form7 min

1.1.6. Geometric Interpretation of Multiplication4 min

1.1.7. Example8 min

1.1.8. Practice1 min

1.1.9. Practice4 min

1.1.10. Fundamental Theorem of Algebra5 min

1.1.11. Practice Level 12 min

1.2.1. Basics of Vectors5 min

1.2.2. Example1 min

1.2.3. Example1 min

1.2.4. Practice2 min

1.2.5. Vector Operations8 min

1.2.10. Practice2 min

1.2.11. Practice (Tricky)5 min

1.2.12. Vector Properties4 min

1.2.13. Example3 min

1.2.14. Example3 min

1.2.15. Practice: Vector Properties2 min

1.2.16. Basics of Dot Product2 min

1.2.17. Example2 min

1.2.18. Practice1 min

1.2.19. Dot Product Properties3 min

1.2.20. Example57 sec

1.2.21. Example2 min

1.2.22. Practice2 min

1.2.23. Practice2 min

1.2.24. Angle Between Vectors3 min

1.2.25. Example2 min

1.2.26. Example2 min

1.2.27. Practice: Dot Product & Angle2 min

1.2.28. Practice2 min

1.2.29. Practice

1.2.30. Projection and Perpendicular3 min

1.2.31. Example2 min

1.2.32. Example3 min

1.2.33. Practice

1.2.34. Practice3 min

1.2.35. Practice: Projections

1.3.1. Lines in

\reals^n

1.3.7. Equations of Planes in

\reals^3

5 min

1.3.8. Example2 min

1.3.9. Example4 min

1.3.10. Practice2 min

1.3.11. Practice

1.3.12. Practice (Tricky)4 min

1.3.13. Cross Product4 min

1.3.14. Example3 min

1.3.15. Practice2 min

1.3.16. Cross Product Properties4 min

1.3.17. Example2 min

1.3.18. Example2 min

1.3.19. Practice2 min

1.3.20. Practice2 min

1.3.21. Finding the Equation of a Plane in R32 min

1.3.22. Example: Finding Equation of Plane in R3 Given 2 Lines2 min

1.3.23. Example: Finding Equation of a Plane in R3 Given 3 Points2 min

1.3.24. Cross Product and Volumes4 min

1.3.25. Area of Parallelograms and Triangles1 min

1.3.26. Example: Cross Product and Area1 min

1.3.27. Triple product2 min

1.3.28. Example: Volume of a Parallelepiped46 sec

1.3.29. Example: Intersection of 2 planes2 min

1.3.30. Hyperplanes3 min

1.3.31. Example1 min

1.3.32. Practice3 min

2. Vector Spaces (Chapters 4-10)

1.5hr

2.1.1. Vector Spaces8 min

2.2.1. Subspaces4 min

2.4.1. Linear Independence6 min

2.4.2. Example2 min

2.4.3. Example1 min

2.4.4. Practice3 min

2.5.1. Example: Spanning Set Contains Basis5 min

2.5.2. Bases2 min

2.5.3. Example: Bases4 min

2.5.4. Dimension1 min

2.6.1. Basis and Dimension3 min

2.6.2. Example4 min

2.6.3. Basis and Dimension3 min

2.7.1. Basis Theorems3 min

2.7.2. Example: Geometry of Dimension3 min

3. Solving Linear Systems (Chapters 11-18)

2.8hr

3.1.1. Basics of Systems of Linear Equations8 min

3.1.2. Example3 min

3.1.3. Practice2 min

3.1.4. Practice3 min

3.1.5. Geometric Interpretation of Solutions to SLEs4 min

3.1.6. Example3 min

3.1.7. Practice3 min

3.2.1. Echelon Forms5 min

3.2.7. Reducing a Matrix5 min

3.2.8. Example3 min

3.2.9. Example7 min

3.2.10. Practice2 min

3.2.11. Practice3 min

3.2.12. Practice

3.2.13. Augmented Matrix3 min

3.2.14. Example3 min

3.2.15. Example1 min

3.2.16. Practice2 min

3.2.17. Practice2 min

3.3.1. Rank of a Matrix5 min

3.3.2. Example3 min

3.3.3. Practice38 sec

3.3.4. Practice1 min

3.4.1. Matrix Multiplication6 min

3.4.7. Solving Matrix Equations2 min

3.4.8. Example52 sec

3.4.9. Example4 min

3.4.10. Practice2 min

3.4.11. Practice54 sec

3.4.12. Practice2 min

3.5.1. Basics of Matrices3 min

3.5.2. Matrix Arithmetic3 min

3.5.3. Example1 min

3.5.4. Practice2 min

3.6.1. Column Space and Null Space (Range and Kernel)3 min

3.6.2. Example

3.6.3. Practice3 min

3.7.1. Solving Linear Systems5 min

3.7.2. Homogeneous Systems2 min

3.8.1. Matrix Inverse4 min

3.8.2. Example3 min

3.8.3. Practice32 sec

3.8.4. Practice2 min

3.8.5. Matrix Inverse Algorithm3 min

3.8.6. Example2 min

3.8.7. Example2 min

3.8.8. Practice2 min

3.8.9. Invertible Matrix Theorem2 min

3.8.10. Example1 min

3.8.11. Practice1 min

4. Orthogonality (Chapters 19-20)

12min

4.1.1. Orthonormal Set3 min

4.1.2. Example2 min

4.1.3. Gram-Schmidt Process3 min

4.1.4. Example4 min

4.1.5. Practice

4.2.1. Orthogonal Matrices

4.2.2. Orthogonal Complement

4.2.3. Orthogonal Projection

5. Determinants, Eigen-Everything, and Diagonalization (Chapters 21-23)

1.9hr

5.1.1. Basics of Determinants5 min

5.1.2. Example2 min

5.1.3. Practice2 min

5.1.4. Practice3 min

5.1.5. Determinant & EROs3 min

5.1.6. Example2 min

5.1.7. Practice2 min

5.1.8. Minors and Cofactors4 min

5.1.9. Determinants of Large Matrices4 min

5.1.10. Example3 min

5.1.11. Practice2 min

5.1.12. Practice4 min

5.1.13. Shortcut for

3 \times 3

Determinants2 min

5.1.14. Example1 min

5.1.15. Practice2 min

5.1.16. Determinants and Inverse3 min

5.1.17. Example3 min

5.1.18. Practice2 min

5.2.1. Eigenvalues and Eigenvectors6 min

5.2.2. Example7 min

5.2.3. Practice8 min

5.2.4. Practice4 min

5.2.5. Complex Eigenvalues

5.2.6. Example

5.2.7. Example

5.2.8. Practice

5.2.9. Properties of Eigenvectors and Eigenvalues3 min

5.2.10. Example3 min

5.2.11. Example6 min

5.2.12. Practice2 min

5.3.1. Diagonalization6 min

5.3.2. Example7 min

5.3.3. Practice2 min

5.3.4. Practice6 min

6. Linear Transformations (Chapter 24)

22min

6.1.1. Linear Transformations6 min

Mock Exams

ME.1. Midterm Exam 1 - Mock Assessment11 Qns

ME.2. Midterm Exam 2 - Mock Assessment14 Qns

ME.3. Final Exam - Mock Assessment32 Qns

MAT 1341

Course Overview

Grade Boosters

1. Algebra and Geometry (Chapters 1-3)

2. Vector Spaces (Chapters 4-10)

3. Solving Linear Systems (Chapters 11-18)

4. Orthogonality (Chapters 19-20)

5. Determinants, Eigen-Everything, and Diagonalization (Chapters 21-23)

6. Linear Transformations (Chapter 24)

Mock Exams

Midterm Exam 3 Overview

Course Notes