1. Module 1: Systems of Equations

1.8hr

1.1.1. Basics of Systems of Linear Equations8 min

1.1.2. Example3 min

1.1.3. Practice2 min

1.1.4. Practice3 min

1.2.1. Augmented Matrix3 min

1.3.1. Echelon Forms5 min

1.4.1. Reducing a Matrix5 min

1.5.1. Rank of a Matrix5 min

1.5.2. Example3 min

1.5.3. Practice38 sec

1.5.4. Practice1 min

1.6.1. Solving Linear Systems5 min

1.6.2. Homogeneous Systems2 min

1.7.1. Geometric Interpretation of Solutions to SLEs4 min

1.7.2. Example3 min

1.7.3. Practice3 min

1.8.1. Polynomial Interpolation5 min

1.8.2. Example4 min

1.8.3. Practice4 min

2. Module 2: Matrices - Matrix Arithmetic

1.5hr

2.1.1. Basics of Matrices3 min

2.1.2. Matrix Arithmetic3 min

2.1.3. Example1 min

2.1.4. Practice2 min

2.2.1. Matrix Multiplication6 min

2.3.1. Matrix Transpose3 min

2.3.2. Symmetric Matrices3 min

2.3.3. Example3 min

2.3.4. Practice60 sec

2.3.5. Practice2 min

2.4.1. Matrix Inverse4 min

2.4.2. Example3 min

2.4.3. Practice32 sec

2.4.4. Practice2 min

2.5.1. Matrix Inverse Algorithm3 min

2.5.2. Example2 min

2.5.3. Example2 min

2.5.4. Practice2 min

2.6.1. Elementary Matrices7 min

2.7.1. Invertible Matrix Theorem2 min

2.7.2. Example1 min

2.7.3. Practice1 min

2.8.1. Solving Matrix Equations2 min

2.8.2. Example52 sec

2.8.3. Example4 min

2.8.4. Practice2 min

2.8.5. Practice54 sec

2.8.6. Practice2 min

3. Module 3: Determinants - Basic Techniques and Properties

41min

3.1.1. Basics of Determinants5 min

3.1.2. Example2 min

3.1.3. Practice2 min

3.1.4. Practice3 min

3.2.1. Determinant & EROs3 min

3.2.2. Example2 min

3.2.3. Practice2 min

3.3.1. Minors and Cofactors4 min

3.3.2. Determinants of Large Matrices4 min

3 \times 3

Determinants2 min

3.4.2. Example1 min

3.4.3. Practice2 min

4. Module 3: Determinants - Applications

16min

4.1.1. Determinants and Inverse3 min

4.1.2. Example3 min

4.1.3. Practice2 min

4.2.1. Cramer's Rule3 min

4.2.2. Example2 min

4.2.3. Practice3 min

5. Module 4: $\mathbb{R}^n$ -Vectors - Distance - $\mathbb{R}^n$ Parametric Lines

1.8hr

5.1.1. Basics of Vectors5 min

5.1.2. Example1 min

5.1.3. Example1 min

5.1.4. Practice2 min

5.2.1. Vector Operations8 min

5.2.7. Practice (Tricky)5 min

5.3.1. Vector Properties4 min

5.3.2. Example3 min

5.3.3. Example3 min

5.3.4. Practice: Vector Properties2 min

5.4.1. Vector Norm5 min

5.5.1. Unit Vectors5 min

5.5.2. Example2 min

5.5.3. Practice2 min

5.6.1. Lines in

\reals^n

5.7.1. Intersection of Two Lines3 min

6. Module 4: $\mathbb{R}^n$ -Dot Product - Projection - Shortest Distance

57min

7. Module 4: $\mathbb{R}^n$ -Planes - $\mathbb{R}^n$ Cross Product

1.1hr

7.1.1. Equations of Planes in

\reals^3

7.1.6. Practice (Tricky)4 min

7.2.1. Hyperplanes3 min

7.2.2. Example1 min

7.2.3. Practice3 min

7.3.1. Intersection of Lines and Planes2 min

7.4.1. Cross Product4 min

7.4.2. Example3 min

7.4.3. Practice2 min

7.5.1. Cross Product Properties4 min

7.6.1. Cross Product and Area2 min

7.6.2. Example3 min

7.6.3. Practice4 min

7.7.1. Volume of a Parallelepiped1 min

7.7.2. Example2 min

7.7.3. Practice1 min

8. Module 5: Linear Transformations - Matrix of a Transformation - Properties

32min

8.1.1. Linear Transformations6 min

8.2.1. Composition and Inverse3 min

8.2.2. Example4 min

8.2.3. Practice3 min

9. Module 5: Special Transformations

17min

9.1.1. Special Linear Transformations in

\reals^2

10. Module 6: Complex Numbers

22min

10.1.1. Basics of Complex Numbers4 min

10.1.2. Operations With Complex Numbers9 min

10.1.3. Example5 min

10.1.4. Practice3 min

11. Module 6: Complex Numbers - Polar Form - Roots

59min

11.1.1. Polar Form7 min

11.1.2. Geometric Interpretation of Multiplication4 min

11.1.3. Example8 min

11.1.4. Practice1 min

11.1.5. Practice4 min

11.2.1. Powers and Root6 min

11.2.2. Example3 min

11.2.3. Example4 min

11.2.4. Practice2 min

11.2.5. Practice3 min

11.3.1. Quadratic Formula3 min

11.3.2. Example3 min

11.3.3. Example7 min

11.3.4. Practice3 min

12. Module 7: Spectral Theory - Eigenvalues and Eigenvectors - Diagonalization

1hr

12.1.1. Eigenvalues and Eigenvectors6 min

12.1.2. Example7 min

12.1.3. Practice8 min

12.1.4. Practice4 min

12.2.1. Complex Eigenvalues

12.2.2. Example

12.2.3. Example

12.2.4. Practice

12.3.1. Properties of Eigenvectors and Eigenvalues3 min

12.3.2. Example3 min

12.3.3. Example6 min

12.3.4. Practice2 min

12.4.1. Diagonalization6 min

12.4.2. Example7 min

12.4.3. Practice2 min

12.4.4. Practice6 min

13. Module 7: Spectral Theory - Diagonalization - Applications

42min

13.1.1. Markov Chains (Random Walks)7 min

13.1.2. Example6 min

13.1.3. Practice5 min

13.2.1. Linear Dynamical Systems and Recurrence Relations9 min

13.2.2. Example7 min

13.2.3. Practice8 min

Mock Exams

ME.1. Mock Final35 Qns

ME.2. Midterm 1 - Mock Assessment23 Qns

ME.3. Midterm 2 - Mock Assessment20 Qns

ME.4. Final Examination - Mock Assessment40 Qns

MATH 211

Course Overview

Grade Boosters

1. Module 1: Systems of Equations

2. Module 2: Matrices - Matrix Arithmetic

3. Module 3: Determinants - Basic Techniques and Properties

4. Module 3: Determinants - Applications

5. Module 4: $\mathbb{R}^n$ -Vectors - Distance - $\mathbb{R}^n$ Parametric Lines

6. Module 4: $\mathbb{R}^n$ -Dot Product - Projection - Shortest Distance

7. Module 4: $\mathbb{R}^n$ -Planes - $\mathbb{R}^n$ Cross Product

8. Module 5: Linear Transformations - Matrix of a Transformation - Properties

9. Module 5: Special Transformations

10. Module 6: Complex Numbers

11. Module 6: Complex Numbers - Polar Form - Roots

12. Module 7: Spectral Theory - Eigenvalues and Eigenvectors - Diagonalization

13. Module 7: Spectral Theory - Diagonalization - Applications

Mock Exams

Midterm 2 Overview

Course Notes

MATH 211

Course Overview

Grade Boosters

1. Module 1: Systems of Equations

2. Module 2: Matrices - Matrix Arithmetic

3. Module 3: Determinants - Basic Techniques and Properties

4. Module 3: Determinants - Applications

5. Module 4: Rn\mathbb{R}^nRn-Vectors - Distance - Rn\mathbb{R}^nRn Parametric Lines

6. Module 4: Rn\mathbb{R}^nRn-Dot Product - Projection - Shortest Distance

7. Module 4: Rn\mathbb{R}^nRn-Planes - Rn\mathbb{R}^nRn Cross Product

8. Module 5: Linear Transformations - Matrix of a Transformation - Properties

9. Module 5: Special Transformations

10. Module 6: Complex Numbers

11. Module 6: Complex Numbers - Polar Form - Roots

12. Module 7: Spectral Theory - Eigenvalues and Eigenvectors - Diagonalization

13. Module 7: Spectral Theory - Diagonalization - Applications

Mock Exams

Midterm 2 Overview

Course Notes

5. Module 4: $\mathbb{R}^n$ -Vectors - Distance - $\mathbb{R}^n$ Parametric Lines

6. Module 4: $\mathbb{R}^n$ -Dot Product - Projection - Shortest Distance

7. Module 4: $\mathbb{R}^n$ -Planes - $\mathbb{R}^n$ Cross Product