Math 107 Exam 3 Study Guide
Below are recommended topics and problems to study for chapter 4. This list is not comprehensive.
1. Vector Spaces: 4.1 # 1-18, 25-27, TF (a)-(e).
2. Subspaces: 4.2 # 1-6, 15-18, TF (a)-(k).
3. Span and Linear Independence
• Spanning: 4.2 # 7-14, 19, 20, 22.
• Linear independence: 4.3 # 1-14, 17-22, 25-32, TF (a)-(h); 4.4 # 21.
4. Basis and Dimension
• Prove a set is a basis: 4.4 # 1-10, 19, 30, TF (a)-(e); 4.5 # 14
• Expand a linearly independent set to become a basis: 4.5 # 12-13, 15-16.
• Reduce a spanning set to become a basis: 4.5 # 17-18; 4.7 # 14-17.
• Dimension: 4.5 # 1-11, 19, 20, 22-26, TF (a)-(g).
5. Change of Basis and Coordinate Vectors
• Coordinate vectors: 4.4 # 11-18, 22, 27.
• Change of basis: 4.6 # 1-10, 12, 13, 15-21, TF (a)-(d).
6. Row Space, Column Space, and Null Space: 4.7 # 3-13, 20-25, 27, TF (a)-(i).
7. Rank and Nullity: 4.8 # 1-9, 11-21, 25, 29-33, TF (a)-(h).
8. Matrix Transformations
• Computations: 4.9 # 1-39
• Properties: 4.10 # 1-35, TF (a)-(g).