The daily homework assignments are the main part of the course. Homework will be collected once week on Friday, except the first one and the exam week. First collection is Wed Jan 16th. TWO lowest homework will be dropped. No late homework will be graded, and there will be a penalty on the credits.

There will be Supplemental Problems assigned occasionally for homework. The Supplemental Problems will also be posted here, and will be announced in class and by email.

Plan on spending 2–4 hours of homework for each class meeting. You are encouraged to help each other on homework. At the beginning of each class a few minutes will be spent answering homework problems.

All problems given by number are from Linear Algebra with Applications, 8th or 9th edition, by Steven Leon.

Over 80% of the exam problems will be directly from homework assignments.

Questions with * are optional. Optional questions may not be graded, hints or partial solutions to optional questions will be provided here or in class. 10% challenging problems in the exams will be closely related to these optional questions.

• Homework 12: Assignments 27 -- 28. Collection date: Fri, April 26. Last updated, April 23 (1)Key and rubric to HW12. (2)Key to OpHW12.

  • Assignments 27: Sec 5.5, 1, 2, 4, 7(assuming V is R^3). Optional ones: 12*, 14*, 15*.

  • Assignments 28: Sec 5.6, 3, 8.

• Homework 11: Assignments 25 -- 26. Collection date: Fri, April 19. Last updated, April 11. (1)Key and rubric to HW11. (2)Key to OpHW11.

  • Assignments 25: Sec 5.3, 1(a), 3(a). Optional ones: 11*.

  • Assignments 26: Sec 5.4, 1, 2, 15(a)(b). Optional ones: 21*, 23*, 33*.

• Homework 10: Assignments 23 -- 24. Collection date: Fri, April 12. Last updated, April 7. (1)Key and rubric to HW10. (2)Key to OpHW10.

  • Assignments 23: Sec 5.1, 1, 2 (a)(b), 3(a)(c), 17. Optional ones: 18*.

  • Assignments 24: Sec 5.2, 1 (a)(b), find N(A) and N(A^T) only; 2(a). Optional ones: 3*，4*.

• Homework 9: Assignments 20 -- 22. Collection date: Mon, April 1. Last updated, Mar 22. (1)Key and rubric to HW9. (2)Key to OpHW9.

  • Assignments 20: Sec 6.3, 1(e), 2 (a), 5. Optional ones: 4*(a), 19*, 31*(a).

  • Assignments 21: Sec4.1, 1(a)(d)(e), 3, (for 1 and 3, do not need to describe the geometric meaning), 4, 5(b)(c), 6(a)(c), 9(a)(b), 17(a). Optional ones: 2*, 14*, 19*(b) (find kernel only), 22*.

  • Assignments 22: Sec4.2, 2(a)(b), 3(c), 4 (a). Optional ones: 5*, 14*(a)>

• Homework 8: Assignments 18 -- 19. Collection date: Fri, Mar 22. Last updated, Mar 18. (1)Key and rubric to HW8. (2)Key to OpHW8.

  • Assignments 18 for Mar 15 lecture: Sec 6.1, 1(a)(c)(f)(h), 2, 3, 4, 14. Optional ones: 6*,8*,17*.

  • Assignments 19 for Mar 18 lecture: Sec 6.3, 1(a)(c) (e), 2 (a), 5. Optional ones: 4*(a), 19*, 31*(a).

• Homework 7: Assignments 15 -- 17. Collection date: Fri, Mar 15. Last updated, Mar 11. (1)Key and rubric to HW7. (2)Key to OpHW7.

  • Assignments 15 for Feb 25,27 lectures: Sec 3.3, 1(a)(b)(c), 2 (a) (c) (e), 8 (a) (b). Optional ones: 10*

  • Assignments 16 for Feb 27,29 lectures: Sec 3.4, 3, 4, 5, 14 (a)(b)(c)(d). Optional ones: 7*, 13*

  • Assignments 17 for Mar 11 lecture: Sec 3.5, 1 (a), 3 (b)

• Homework 6: Assignments 13 -- 14. Collection date: Wed, Feb 27. Last updated, Feb 25. (1)Key and rubric to HW6. (2)Key to OpHW6.

  • Assignments 13 for Feb 13th lecture: Sec 3.1, 3 (Check Axioms A1-A8), 10, 12, 13

  • Assignments 13 for Feb 20,22 lectures: Sec 3.2, 1 (a)(e), 2 (a), 3 (a)(f), 4 (b)(c), 8, 11 (a)(c), 13 (a). Optional ones: 6* (c)(d), 12*(a)(b), 14*, 19*

• Homework 5: Assignments 11 -- 12. Collection date: Fri, Feb 15. Last updated, Feb 15. Key and rubric to HW5.

  • Assignments 11 for Feb 6th, 8th lectures: Sec 2.1, 1(a)(b), 2(a)(b), 3(a)(c)(e)(g), 5, 6; Optional ones: 8*, 13*, and the case n=2 for 10* (i.e., prove that if A is an 3×3 matrix with two identical rows, then det(A) = 0.)

  • Assignments 12 for Feb 8th, 11th lectures: Sec 2.2, 1 (a)(c); 3 (c)(e)(f); 5, 6, 7; (Hint for 5,6: use Theorem 2.2.3). Optional ones: 12*, 16*, 15*(Hint: use Theorem 2.2.1 to claim the existence of the inverse of A), 16*, 18**,19**

• Homework 4: Assignments 9 -- 10. Collection date: Fri, Feb 8. Last updated, Feb 1. Key and rubric to HW4.

  • Assignments 9 for Feb 1st lecture: Sec 1.4, 12, 13, 15; Optional ones: 16*, 20*, 21* (Solutions).

  • Assignments 10 for Feb 4th lectures: Sec 1.5, 1, 2, 3, 5, 7; Optional ones: 17*, 18* (Solutions).

• Homework 3: Assignments 7 -- 8. Collection date: Fri, Feb 1st. Last updated, Jan 29th. Key and rubric to HW3.

  • Assignments 7 for Jan 23rd, 25th lectures: Sec1.3, 1(d)(e)(h); 2(a)(b)(e); 4(a)(b)(c); 5 (c); 6 (c); 7(b); 8 (b)(c)(d); Optional ones: 9*, 16* (Solutions)

  • Assignments 8 for Jan 28th lecture: Sec 1.4, 7, 9, 11(a)(c)(e), 12, 13, 15; Optional ones: 16*, 20*, 21*. Remark: Problems 12-21 are removed from Homework 3 because of the cancelation of class on Wed. These will be assigned for the next due on Feb 8.

• Homework 2: Assignments 5 -- 6. Collection date: Fri, Jan 25th. Last updated, Jan 23rd. Key and rubric to HW2.

  • Assignments 5 for Jan 16th Wed lecture: Sec1.2, 3(a)(b)(c)(d), 4(a)(b)(c)(d), 5 (e)(f), 7*,8*. Solutions to Op problems

  • Assignments 6 for Jan 18th Fri lecture: Sec1.3, 1(a)(b)(c); 5(a)(b); 6(a)(b); 8(a)

• Homework 1: Collection date: Wed, Jan 16th. Last updated, Jan 11th. Key and rubric to HW1.

  • Assignments 1 for Jan 7th Mon lecture: Section 1.1, Page 10, 1 (a)(c), 2 (a)(c), 3 (a)(c).

  • Assignments 2 for Jan 9th Wed lecture: Section 1.1, Page 10, 4 (a)(c), 5 (c),6 (e).

  • Assignments 3 for Jan 11th Fri lecture: Section 1.1, Page 11, 7*, 9*. SOLUTION TO THE OPTIONAL PROBLEMS.

  • Assignments 4 for Jan 14th Mon lecture: Sec 1.2, Page 23, 1, 2 (a)(c)(d)