1. Linear Equations in Linear Algebra

2.9hr

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

1.1.5. Augmented Matrix3 min

1.2.1. Augmented Matrix3 min

1.3.1. Echelon Forms5 min

1.4.1. Reducing a Matrix5 min

1.5.1. Basics of Vectors5 min

1.5.2. Example1 min

1.5.3. Example1 min

1.5.4. Practice2 min

1.5.5. Vector Properties4 min

1.5.6. Example3 min

1.5.7. Example3 min

1.5.8. Practice: Vector Properties2 min

1.5.9. Vector Operations8 min

1.5.10. Example2 min

1.5.11. Example2 min

1.5.12. Example3 min

1.5.13. Practice1 min

1.5.14. Practice2 min

1.5.15. Practice (Tricky)5 min

1.6.1. Solving Linear Systems5 min

1.6.2. Homogeneous Systems2 min

1.6.3. Wize Concept Clarifier 15 min

1.8.1. Linear Independence6 min

1.8.2. Example2 min

1.8.3. Example1 min

1.8.4. Practice3 min

1.9.1. Linear Transformations6 min

1.9.2. Example2 min

1.9.3. Example3 min

1.10.1. Practice2 min

1.10.2. Practice8 min

2. Linear Transformations

49min

2.1.1. Linear Transformations6 min

2.2.1. Composition and Inverse3 min

2.2.2. Example4 min

2.2.3. Practice3 min

2.3.1. Special Linear Transformations in

\reals^2

3. Matrix Algebra

1.9hr

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. Matrix Inverse4 min

3.4.2. Example3 min

3.4.3. Practice32 sec

3.4.4. Practice2 min

3.5.1. Matrix Inverse Algorithm3 min

3.5.2. Example2 min

3.5.3. Example2 min

3.5.4. Practice2 min

3.6.1. Elementary Matrices7 min

3.7.1. Invertible Matrix Theorem2 min

3.7.2. Example1 min

3.7.3. Practice1 min

3.8.1. Solving Matrix Equations2 min

3.8.2. Example52 sec

3.8.3. Example4 min

3.8.4. Practice2 min

3.8.5. Practice54 sec

3.8.6. Practice2 min

3.9.1. Subspaces4 min

3.9.2. Example3 min

3.9.3. Practice4 min

3.10.1. Rank of a Matrix5 min

3.10.2. Example3 min

3.10.3. Practice38 sec

3.10.4. Practice1 min

4. Determinants

58min

5. Vector Spaces

1.3hr

6. Eigenvalues and Eigenvectors

3hr

6.1.1. Eigenvalues and Eigenvectors6 min

6.1.2. Example7 min

6.1.3. Practice8 min

6.1.4. Practice4 min

6.2.1. Properties of Eigenvectors and Eigenvalues3 min

6.2.2. Example3 min

6.2.3. Example6 min

6.2.4. Practice2 min

6.3.1. Diagonalization6 min

6.3.2. Example7 min

6.3.3. Practice2 min

6.3.4. Practice6 min

6.4.1. Basics of Complex Numbers4 min

6.4.2. Operations With Complex Numbers9 min

6.4.3. Example5 min

6.4.4. Practice3 min

6.5.1. Complex Eigenvalues

6.5.2. Example

6.5.3. Example

6.5.4. Practice

6.6.1. Linear Transformations6 min

6.7.1. Special Linear Transformations in

\reals^2

6.8.1. Markov Chains (Random Walks)7 min

6.8.2. Example6 min

6.8.3. Practice5 min

6.9.1. Linear Dynamical Systems and Recurrence Relations9 min

6.9.2. Example7 min

6.9.3. Practice8 min

6.10.1. Definition of a Linear Differential Equation2 min

6.10.2. Simplest Differential Equation:

y'=ay

5 min

6.10.3. Initial Value Problems2 min

6.10.4. Example2 min

6.10.5. Practice

6.10.6. Practice

6.11.1. Systems of Linear Differential Equations3 min

6.11.2. Solving a System of Linear DEs2 min

6.11.3. Example4 min

6.11.4. Practice

6.11.5. Practice

6.12.1. Higher Order Linear DEs

6.12.2. Example

6.12.3. Practice

6.12.4. Practice

7. Orthogonality and Least Squares

2hr

7.1.1. Vector Norm5 min

7.2.1. Unit Vectors5 min

7.2.2. Example2 min

7.2.3. Practice2 min

7.3.1. Basics of Dot Product2 min

7.3.2. Example2 min

7.3.3. Practice1 min

7.4.1. Dot Product Properties3 min

7.5.1. Angle Between Vectors3 min

7.5.2. Example2 min

7.5.3. Example2 min

7.5.4. Practice: Dot Product & Angle2 min

7.5.5. Practice2 min

7.5.6. Practice

7.6.1. Projection and Perpendicular3 min

7.6.6. Practice: Projections

7.7.1. Orthonormal Set3 min

7.7.2. Example2 min

7.7.3. Gram-Schmidt Process3 min

7.7.4. Example4 min

7.7.5. Practice

7.8.1. Cross Product4 min

7.8.2. Example3 min

7.8.3. Practice2 min

7.9.1. Cross Product Properties4 min

7.10.1. Cross Product and Area2 min

7.10.2. Example3 min

7.10.3. Practice4 min

7.11.1. Volume of a Parallelepiped1 min

7.11.2. Example2 min

7.11.3. Practice1 min

7.12.1. Least Squares Approximation6 min

7.12.2. Example4 min

7.12.3. Example: Least Squares for Polynomials

7.12.4. Practice

Mock Exams

ME.1. Midterm 1 - Mock Assessment24 Qns

ME.2. Midterm 2 - Mock Assessment24 Qns

ME.3. Final Examination - Mock Assessment47 Qns

MATH 1B03

Course Overview

Grade Boosters

1. Linear Equations in Linear Algebra

2. Linear Transformations

3. Matrix Algebra

4. Determinants

5. Vector Spaces

6. Eigenvalues and Eigenvectors

7. Orthogonality and Least Squares

Mock Exams

Test 2 Overview

Course Notes