1. Vector Spaces and Subspaces

1.3hr

1.1.1. Vector Spaces8 min

1.2.1. Subspaces4 min

1.2.2. Example3 min

1.2.3. Practice4 min

1.3.1. Linear Independence6 min

1.5.1. Basis and Dimension3 min

1.5.2. Example4 min

1.5.3. Basis and Dimension3 min

1.5.4. Practice4 min

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

2. Systems of Linear Equations (SLEs) (Linear Systems)

1.8hr

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

2.8.1. Polynomial Interpolation5 min

2.8.2. Example4 min

2.8.3. Practice4 min

3. Linear Transformations

32min

3.1.1. Linear Transformations6 min

3.2.1. Composition and Inverse3 min

3.2.2. Example4 min

3.2.3. Practice3 min

4. Matrices

1.5hr

4.1.1. Basics of Matrices3 min

4.1.2. Matrix Arithmetic3 min

4.1.3. Example1 min

4.1.4. Practice2 min

4.2.1. Matrix Multiplication6 min

4.3.1. Matrix Transpose3 min

4.3.2. Symmetric Matrices3 min

4.3.3. Example3 min

4.3.4. Practice60 sec

4.3.5. Practice2 min

4.4.1. Matrix Inverse4 min

4.4.2. Example3 min

4.4.3. Practice32 sec

4.4.4. Practice2 min

4.5.1. Matrix Inverse Algorithm3 min

4.5.2. Example2 min

4.5.3. Example2 min

4.5.4. Practice2 min

4.6.1. Elementary Matrices7 min

4.7.1. Invertible Matrix Theorem2 min

4.7.2. Example1 min

4.7.3. Practice1 min

4.8.1. Solving Matrix Equations2 min

4.8.2. Example52 sec

4.8.3. Example4 min

4.8.4. Practice2 min

4.8.5. Practice54 sec

4.8.6. Practice2 min

5. Determinants

58min

6. Eigenvalues and Eigenvectors (Spectral Theory)

1.7hr

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. Markov Chains (Random Walks)7 min

6.4.2. Example6 min

6.4.3. Practice5 min

6.5.1. Linear Dynamical Systems and Recurrence Relations9 min

6.5.2. Example7 min

6.5.3. Practice8 min

7. Differential Equations

20min

7.1.1. Definition of a Linear Differential Equation2 min

7.1.2. Simplest Differential Equation:

y'=ay

5 min

7.1.3. Initial Value Problems2 min

7.1.4. Practice

7.1.5. Practice

7.1.6. Example2 min

7.2.1. Systems of Linear Differential Equations3 min

7.2.2. Solving a System of Linear DEs2 min

7.2.3. Example4 min

7.2.4. Practice

7.2.5. Practice

7.3.1. Higher Order Linear DEs

7.3.2. Example

7.3.3. Practice

7.3.4. Practice

8. Cryptography (COMING SOON)

9. Orthogonality

12min

9.1.1. Orthonormal Set3 min

9.1.2. Example2 min

9.1.3. Gram-Schmidt Process3 min

9.1.4. Example4 min

9.1.5. Practice

9.2.1. Orthogonal Matrices

9.2.2. Orthogonal Complement

9.2.3. Orthogonal Projection

10. Least Squares Approximation

10min

10.1.1. Least Squares Approximation6 min

10.1.2. Example4 min

10.1.3. Example: Least Squares for Polynomials

10.1.4. Practice

Mock Exams

ME.1. Midterm 1 - Mock Assessment7 Qns

ME.2. Midterm 2 - Mock Assessment8 Qns

ME.3. Final Exam - Mock Assessment10 Qns

APSC 174

Course Overview

1. Vector Spaces and Subspaces

2. Systems of Linear Equations (SLEs) (Linear Systems)

3. Linear Transformations

4. Matrices

5. Determinants

6. Eigenvalues and Eigenvectors (Spectral Theory)

7. Differential Equations

8. Cryptography (COMING SOON)

9. Orthogonality

10. Least Squares Approximation

Mock Exams

ME.1 Midterm 1 - Mock Assessment

Included in Wizeprep Plus

Midterm 1 - Mock Assessment

Timer