1. The Vector Space $\mathbb{R}^n$

1.5hr

1.1.1. Basics of Vectors5 min

1.1.2. Example1 min

1.1.3. Example1 min

1.1.4. Practice2 min

1.1.5. Vector Properties4 min

1.1.6. Example3 min

1.1.7. Example3 min

1.1.8. Practice: Vector Properties2 min

1.2.1. Vector Operations8 min

1.2.7. Practice (Tricky)5 min

1.3.1. Vector Norm5 min

1.3.6. Unit Vectors5 min

1.3.7. Example2 min

1.3.8. Practice2 min

1.4.1. Lines in

\reals^n

2. The Vector Space $\mathbb{C}$

1.3hr

2.1.1. Basics of Complex Numbers4 min

2.1.2. Operations With Complex Numbers9 min

2.1.3. Example5 min

2.1.4. Practice3 min

2.2.1. Polar Form7 min

2.2.2. Geometric Interpretation of Multiplication4 min

2.2.3. Example8 min

2.2.4. Practice1 min

2.2.5. Practice4 min

2.3.1. Powers and Root6 min

2.4.1. Quadratic Formula3 min

2.4.2. Example3 min

2.4.3. Example7 min

2.4.4. Practice3 min

3. Dot Products and Orthogonal Projections

38min

4. Linear Equations and Hyperplanes

1.2hr

5. Systems of Linear Equations

1.4hr

6. Matrix Operations

1.2hr

6.1.1. Basics of Matrices3 min

6.1.2. Matrix Arithmetic3 min

6.1.3. Example1 min

6.1.4. Practice2 min

6.1.5. Matrix Transpose3 min

6.1.6. Matrix Multiplication6 min

6.1.7. Example1 min

6.1.8. Example4 min

6.1.9. Practice3 min

6.1.10. Practice2 min

6.1.11. Practice

6.2.1. Matrix Inverse4 min

6.2.2. Example3 min

6.2.3. Practice32 sec

6.2.4. Practice2 min

6.2.5. Invertible Matrix Theorem2 min

6.2.6. Example1 min

6.2.7. Practice1 min

6.3.1. Matrix Inverse Algorithm3 min

6.3.2. Example2 min

6.3.3. Example2 min

6.3.4. Practice2 min

6.4.1. Solving Matrix Equations2 min

6.4.2. Example52 sec

6.4.3. Example4 min

6.4.4. Practice2 min

6.4.5. Practice54 sec

6.4.6. Practice2 min

6.5.1. Symmetric Matrices3 min

6.5.2. Example3 min

6.5.3. Practice60 sec

6.5.4. Practice2 min

7. Determinants

50min

7.1.1. Minors and Cofactors4 min

7.1.2. Shortcut for

3 \times 3

Determinants2 min

7.1.3. Example1 min

7.1.4. Practice2 min

7.2.1. Determinants of Large Matrices4 min

7.2.2. Example3 min

7.2.3. Practice2 min

7.2.4. Practice4 min

7.3.1. Basics of Determinants5 min

7.3.2. Example2 min

7.3.3. Practice2 min

7.3.4. Practice3 min

7.3.5. Determinant & EROs3 min

7.3.6. Example2 min

7.3.7. Practice2 min

7.3.8. Determinants and Inverse3 min

7.3.9. Example3 min

7.3.10. Practice2 min

8. Cross Product

34min

8.1.1. Cross Product4 min

8.1.2. Example3 min

8.1.3. Practice2 min

8.1.4. Cross Product Properties4 min

8.2.1. Cross Product and Area2 min

8.2.2. Example3 min

8.2.3. Practice4 min

8.2.4. Volume of a Parallelepiped1 min

8.2.5. Example2 min

8.2.6. Practice1 min

9. Vector Spaces

50min

9.1.1. Vector Spaces8 min

9.2.1. Subspaces4 min

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

9.3.2. Example

9.3.3. Practice3 min

10. Basis and Dimension

35min

10.1.1. Linear Independence6 min

10.1.2. Example2 min

10.1.3. Example1 min

10.1.4. Practice3 min

10.3.1. Basis and Dimension3 min

10.3.2. Example4 min

10.3.3. Basis and Dimension3 min

10.3.4. Practice4 min

10.4.1. Rank of a Matrix5 min

10.4.2. Example3 min

10.4.3. Practice38 sec

10.4.4. Practice1 min

11. Change of Basis

24min

11.1.1. Change of Basis6 min

11.1.2. Example: Change of Basis3 min

11.1.3. Practice Question: Change of Basis3 min

11.2.1. Orthonormal Set3 min

11.2.2. Example2 min

11.3.1. Gram-Schmidt Process3 min

11.3.2. Example4 min

11.3.3. Practice

11.4.1. Orthogonal Complement

11.4.2. Orthogonal Projection

12. Linear Transformations

1.3hr

13. Eigenvalues and Eigenvectors

1.1hr

13.1.1. Eigenvalues and Eigenvectors6 min

13.1.2. Example7 min

13.1.3. Practice8 min

13.1.4. Practice4 min

13.1.5. Properties of Eigenvectors and Eigenvalues3 min

13.1.6. Example3 min

13.1.7. Example6 min

13.1.8. Practice2 min

13.2.1. Diagonalization6 min

13.2.2. Example7 min

13.2.3. Practice2 min

13.2.4. Practice6 min

13.3.1. Example: Orthogonal Diagonalization6 min

13.4.1. Complex Eigenvalues

13.4.2. Example

13.4.3. Example

13.4.4. Practice

Mock Exams

ME.1. Midterm Exam - Mock Assessment14 Qns

ME.2. Final Exam - Mock Assessment19 Qns

MATH 102

Course Overview

1. The Vector Space $\mathbb{R}^n$

2. The Vector Space $\mathbb{C}$

3. Dot Products and Orthogonal Projections

4. Linear Equations and Hyperplanes

5. Systems of Linear Equations

6. Matrix Operations

7. Determinants

8. Cross Product

9. Vector Spaces

10. Basis and Dimension

11. Change of Basis

12. Linear Transformations

13. Eigenvalues and Eigenvectors

Mock Exams

ME.2 Final Exam - Mock Assessment

Included in Wizeprep Plus

Final Exam - Mock Assessment

Timer

MATH 102

Course Overview

1. The Vector Space Rn\mathbb{R}^nRn

2. The Vector Space C\mathbb{C}C

3. Dot Products and Orthogonal Projections

4. Linear Equations and Hyperplanes

5. Systems of Linear Equations

6. Matrix Operations

7. Determinants

8. Cross Product

9. Vector Spaces

10. Basis and Dimension

11. Change of Basis

12. Linear Transformations

13. Eigenvalues and Eigenvectors

Mock Exams

ME.2 Final Exam - Mock Assessment

Included in Wizeprep Plus

Final Exam - Mock Assessment

Timer

1. The Vector Space $\mathbb{R}^n$

2. The Vector Space $\mathbb{C}$