Matrices and Linear
Transformations 21-241 Spring, 2013 J. Iovino |

A course outline and a general description of the policies of the course is available here

For row reduction, P. Bogacki's Linear Algebra Toolkit is useful and easy to use. Thanks to P. Bogacki for making these scripts freely available.

For more complex matrix operations (multiplication, inversion, etc.), I recommend WolframAlpha.

- 1/14: Introduction. Sections 1.1 and 1.2.

- Due 1/23. Page 9: 1-5, 7, 8, 13, 16-19.
- 1/16: Section 1.3.
- Due 1/23. Page 15: 3-5, 10, 11, 14, 18, 28.
- 1/18: Finished Section 1.3, started Section 1.4.
- Due 1/23. Page 25: First part (that is, only the first multiplication) of exercises 1-3.
- 1/21: Finished Section 1.4.
- Due 1/30. Page 27:10-13, 17, 21, 38, 39.
- 1/23: Section 1.6, with emphasis on proofs.
- Due 1/30. Page 52: 4, 28, 29, 30.
- 1/25: Quiz 1. Section 1.6
- 1/28: Section 1.6
- Due 2/6. Page 29: 28, 36. Page 52: third part of 6, 11, third part of 10.
- 1/30: Section 1.6
- Due 2/6. Page 55: 40. Page 65: 1.12. (In this last question, "reason" means "proof".)
- 2/1: Quiz 2. More examples of proofs.
- 2/4: Section 2.1. Proofs using the vector space axioms.
- Due 2/13. Section 2.1 (Page 73): 2, 5, 7.
- 2/6: Section 2.1. Subspaces.
- Due 2/13. Section 2.1 page 73): 4, 10, 11, 14, 20.
- 2/8: Quiz 3. More subspaces.
- Due 2/13. Section 2.1 (page 73): 27, 28, 30, 31.
- 2/11: Test 1.
- 2/13: Remarks on Test 1 and Quiz 3. Started Section 2.2.
- 2/15 Section 2.2, with emphasis on proofs.
- No homework due 2/20.
- 2/18: Finished Section 2.2.
- Due 2/27. Section 2.2 (page 85): 4, 5, 12, 13, 15, 21, 24, 25, 38, 39, 44, 45.
- 2/20: Section 2.3.
- Due 2/27. Section 2.3 (page 98): 4, 5, 8, 9, 11, 20, 28 (prove or disprove your assertions mathematically).
- 2/22: Section 2.3.
- Due 2/27. Section 2.3 (page 98): 31, 35, 37.
- 2/25: Section 2.3. (Proofs of the main theorems of the section.)
- 2/27: Section 2.3. (Proofs of the main theorems of the section.)
- 3/1: Section 2.3. (Finished proving the main theorems of the section.)
- 3/4: Test 2.
- 3/6: Started Section 2.6.
- Due 3/20. Section 2.6 (page 133): 3, 4 (give a precise proof of this statement), 5, 6, 14, 21, 22.
- 3/20: Section 2.6, continued.
- Due 3/27. Section 2.6 (page 133): 42, 44, 49, 50 (prove your assertions).
- 3/22: Finished Section 2.6.
- Due 3/27. Section 2.6 (page 133): 7, 8.
- 3/25: Started Section 3.1. Course surveys.
- Due 4/3. Section 3.1 (page 148): 2, 14. (Note that in Exercise 14 you need two separate proofs.)
- 3/27: Quiz 4. Section 3.1, continued.
- Due 4/3. Section 3.1 (page 148): 15, 17, 18, 19, 41, 44, 46.
- 3/29: Section 3.4.
- Due 4/3. Section 3.4 (page 185): 28, 29. Section 3.1 (page 148): 8.
- 4/1: Finished Chapter 3 (examples).
- 4/3: Quiz 5. Started Chapter 4.
- 4/8: Section 4.2
- Due 4/17. Section 4.2 (page 206): 12, 14, 21, 26, 27, 28.
- 4/10: Section 4.2, continued
- Due 4/17. Section 4.2 (page 206): 19.
- 4/12: Section 4.3
- Due 4/24. Section 4.3 (page 215): 3-7
- 4/15: Test 3
- 4/17: Section 4.3
- Due 4/24. Section 4.3 (page 215): 15, 16, 18, 22.
- 4/19: Section 4.3
- 4/22: Section 4.4
- Due 5/3. Section 4.3 (page 215): 3. Section 4.4 (page 225): 14(b), 17.
- 4/24: Section 5.1
- 4/26: Section 5.2
- Due 5/3. Section 5.2 (page 250): 4, 6, 8, 15, 18, 19, 21, 25, 29, 30, 34.
- 4/30: Proofs of the theorems in 5.2.
- 5/1: Conclusion and review.

Office hours: MWF, 1-2 pm, and by appointment.