NMM 1411A/B

UWO

Course Overview

Lessons & Practice

I. Welcome

54 sec

1. Systems of Linear Equations and Matrices

4hr

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. Solving Linear Systems5 min

1.1.6. Homogeneous Systems2 min

1.1.7. Example3 min

1.1.8. Example5 min

1.1.9. Practice2 min

1.1.10. Practice5 min

1.1.11. Geometric Interpretation of Solutions to SLEs4 min

1.1.12. Example3 min

1.1.13. Practice3 min

1.2.1. Augmented Matrix3 min

1.2.6. Echelon Forms5 min

1.2.12. Reducing a Matrix5 min

1.2.13. Example3 min

1.2.14. Example7 min

1.2.15. Practice2 min

1.2.16. Practice3 min

1.2.17. Practice

1.3.1. Basics of Matrices3 min

1.3.2. Matrix Arithmetic3 min

1.3.3. Example1 min

1.3.4. Practice2 min

1.3.5. Matrix Multiplication6 min

1.4.1. Matrix Inverse4 min

1.4.2. Example3 min

1.4.3. Practice32 sec

1.4.4. Practice2 min

1.4.5. Invertible Matrix Theorem2 min

1.4.6. Example1 min

1.4.7. Practice1 min

1.5.1. Matrix Inverse Algorithm3 min

1.5.2. Example2 min

1.5.3. Example2 min

1.5.4. Practice2 min

1.5.5. Elementary Matrices7 min

1.6.1. Rank of a Matrix5 min

1.6.2. Example3 min

1.6.3. Practice38 sec

1.6.4. Practice1 min

1.6.5. Solving Matrix Equations2 min

1.6.6. Example52 sec

1.6.7. Example4 min

1.6.8. Practice2 min

1.6.9. Practice54 sec

1.6.10. Practice2 min

1.7.1. Matrix Transpose3 min

1.7.2. Symmetric Matrices3 min

1.7.3. Example3 min

1.7.4. Practice60 sec

1.7.5. Practice2 min

1.8.1. Linear Transformations6 min

1.8.6. Composition and Inverse3 min

1.8.7. Example4 min

1.8.8. Practice3 min

2. Determinants

52min

2.1.1. Minors and Cofactors4 min

2.1.2. Determinants of Large Matrices4 min

2.1.3. Example3 min

2.1.4. Practice2 min

2.1.5. Practice4 min

2.3.1. Basics of Determinants5 min

2.3.2. Example2 min

2.3.3. Practice2 min

2.3.4. Practice3 min

2.3.5. Determinant & EROs3 min

2.3.6. Example2 min

2.3.7. Practice2 min

2.3.8. Determinants and Inverse3 min

2.3.9. Example3 min

2.3.10. Practice2 min

2.3.11. Cramer's Rule3 min

2.3.12. Example2 min

2.3.13. Practice3 min

3. Euclidean Vector Spaces

2.2hr

3.1.1. Basics of Vectors5 min

3.1.2. Example1 min

3.1.3. Example1 min

3.1.4. Practice2 min

3.1.5. Vector Properties4 min

3.1.6. Example3 min

3.1.7. Example3 min

3.1.8. Practice: Vector Properties2 min

3.1.9. Vector Operations8 min

3.1.10. Example2 min

3.1.11. Example2 min

3.1.12. Example3 min

3.1.13. Practice1 min

3.1.14. Practice2 min

3.1.15. Practice (Tricky)5 min

3.3.1. Projection and Perpendicular3 min

3.3.6. Practice: Projections

3.3.7. Orthonormal Set3 min

3.3.8. Example2 min

4. General Vector Spaces

2.4hr

4.1.1. Vector Spaces8 min

4.2.1. Subspaces4 min

4.2.2. Example3 min

4.2.3. Practice4 min

4.3.1. Linear Independence6 min

4.5.1. Basis and Dimension3 min

4.5.2. Example4 min

4.5.3. Basis and Dimension3 min

4.5.4. Practice4 min

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

4.7.2. Example

4.7.3. Practice3 min

4.8.1. Matrix Rank11 min

4.8.2. Example: Rank-Nullity3 min

4.8.3. Example: Rank-Nullity Theorem13 min

4.8.4. Rank of a Matrix5 min

4.8.5. Rank of a Matrix3 min

4.8.6. Example: Rank of a Matrix2 min

4.8.7. Example: Rank4 min

4.9.1. Special Linear Transformations in

\reals^2

4.9.5. Concept Clarifier6 min

5. Eigenvalues and Eigenvectors

1hr

5.1.1. Eigenvalues and Eigenvectors6 min

5.1.2. Example7 min

5.1.3. Practice8 min

5.1.4. Practice4 min

5.1.5. Properties of Eigenvectors and Eigenvalues3 min

5.1.6. Example3 min

5.1.7. Example6 min

5.1.8. Practice2 min

5.2.1. Diagonalization6 min

5.2.2. Example7 min

5.2.3. Practice2 min

5.2.4. Practice6 min

6. Inner Product Spaces

7min

6.3.1. Gram-Schmidt Process3 min

6.3.2. Example4 min

6.3.3. Practice

6.3.4. Orthogonal Matrices

6.3.5. Orthogonal Complement

6.3.6. Orthogonal Projection

Mock Exams

ME.1. Test 1 - Mock Assessment11 Qns

ME.2. Test 2 - Mock Assessment7 Qns

ME.3. Final Exam - Mock Assessment21 Qns

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ME.3 Final Exam - Mock Assessment

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Final Exam - Mock Assessment

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