2. Systems of linear equations 10. Gaussian elimination
11. Reduced row echelon form
12. Computing inverses
13. Elementary matrices
14. LU decomposition
15. Solving (LU)x = b

3. Vector spaces 16. Vector spaces
17. Linear independence
18. Span, basis and dimension
19. Gram-Schmidt process
20. Gram-Schmidt process example
21. Null space
22. Application of the null space
23. Column space
24. Row space, left null space and rank
25. Orthogonal projections
26. The least-squares problem
27. Solution of the least-squares problem

4. Eigenvalues and eigenvectors 28. Two-by-two and three-by-three determinants
29. Laplace expansion
30. Leibniz formula
31. Properties of a determinant
32. The eigenvalue problem
33. Finding eigenvalues and eigenvectors (1)
34. Finding eigenvalues and eigenvectors (2)
35. Matrix diagonalization
36. Matrix diagonalization example
37. Powers of a matrix
38. Powers of a matrix example
Problem Solution