MTH 420/520--A 2nd Course in Linear Algebra--Homework Assignments

Exams:

• Exam I: Friday, Feb 27 completed
  
• Exam II: Friday, March 27 completed
• Exam III: Friday, May 1 completed
• Final Exam: Monday, May 11,  11:45 AM - 2:45 PM in NSC 218
  

Textbook: 

• Linear Algebra (2nd Edition) by Kenneth M Hoffman and Ray Kunze

Note: problems in brackets [ ] are to be done, but not turned in.

Final Exam

• When: Monday, May 11,  11:45 AM - 2:45 PM
• Where: NSC 218
• Covers: Sections 1.1 - 3.5, 3.7, 4.1 - 5.2, 5.3 (Statement of Theorem 2; Theorem 3 and proof), 5.4, 6.1 - 6.4, 6.6
• including the corresponding material on the lecture slides/notes
• including the Cayley-Hamilton Theorem
• Format: 1 to 3 definitions or statements of result, 6 - 9 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• Review Session: Sunday, May 10, 1:00 PM in Math 250 [come in thru the Bridge if you don't have card access]

Coming Attractions (tentative list of upcoming assignments):

• Final Exam

Assignment 1--Due Friday, January 30:

• Recitation for 420: Recitation will not meet  Monday, January 26, at 8:00 AM in Math 150
• Quiz (420): Quiz on Monday, February 2. Topics: 1.1 - 1.4 (through Theorem 5)
  
• Section 1.2:  1 - 4
• Note: problems listed for an assignment are to be handed in class on the due date. You may type them in LaTeX (required for graduate students)

Assignment 2--Due Wednesday, February 4:

• Recitation for 420: Recitation will meet  Monday, February 2, at 8:00 AM in Math 150
• Quiz (420): Quiz in recitation on Monday, February 2: Topics: 1.1 - 1.4 (through Theorem 5)
•  including the corresponding material on the lecture slides/notes
  
• Format for Quiz: one definition or statement of result (memorize these); one problem or proof.
  
• Section 1.3:  3, 5
• Section 1.4:  1, 4, 8, 10
• Section 1.5:  3, [6], 8 Problems in brackets should be done, but not turned in

Assignment 3--Due Wednesday, February 11:

• Quiz (420): Quiz in recitation on Monday, February 9: Topics: 1.4 - 2.2 (through top of p. 37)
•  including the corresponding material on the lecture slides/notes
  
• Section 1.5:  4
• Section 1.6: 1, 5 - 7, 10, [11]. Look at 12 (extremely hard problem)
• Section 2.1: 4, 6, [7]
• Section 2.2: [1 - 2],  3, 5, 7,  9
• Problem 3 has a misprint; should be R^4 not R^5

Assignment 4--Due Wednesday, February 18:

• Quiz (420): Quiz in recitation on Monday, February 16: Topics: 2.2 - 2.4
  
•  including the corresponding material on the lecture slides/notes
  
• Section 2.3: [ 1], 4, 7, 9 - 11, 13, 14 (a harder, but still doable problem)
• Note: (Problem 13 references Exercise 5 in Section 1.2—not 1.1)
• Section 2.4: 1, 2, 4, 6

Assignment 5--Due Wednesday, February 25:

• Quiz (420): Quiz in recitation on Monday, February 23: Topics: 2.5, 2.6, 3.1
  
•  including the corresponding material on the lecture slides/notes
  
• Section 2.6: 1, [2], 3, 5
• For Problem 1:  Theorem 4 is on p 44
• Note: Example 22 in Section 2.6 has been posted UBLearns>Course Documents>Matrix Manipulation
• Section 3.1: 2, 4, 5, 8, 10, 12
• Note [added after assignment turned in]: The example for problem 12 should be in the context of a general vector space of dim n over a field F

Assignment 6--Due Wednesday, March 4:

• Quiz (420): No Quiz in recitation on Monday, March 2: Topics: none
  
•  including the corresponding material on the lecture slides/notes
  
• Section 3.2: 3 - 6, 8
• Section 3.2: 10, 11
• Section 3.3: 2, 3, 5, 7

Assignment 7--Due Wednesday, March 11:

• Quiz (420): Quiz in recitation on Monday, March 9: Topics: 3.2 - 3.5 [through Theorem 15]
  [depending on where we end on Friday]
•  including the corresponding material on the lecture slides/notes
  
• Section 3.3: 6
• Section 3.4: 2, 5, 10, 12
• Section 3.5: 1 - 5
• For problem 2, the answer should be in terms of the standard ordered basis for the dual space
• where the standard ordered basis for the dual space is the dual basis to the standard ordered basis for C^3.
• alternatively, the book thinks of C^3 as row vectors, so the dual basis should be actual column vectors
• that give \delta_{ij}, the Kronecker delta, when applied to the given basis.

Assignment 8--Due Wednesday, March 25:

• Quiz (420): Quiz in recitation on Monday, March 23: Topics: 3.5 [through Theorem 16 on p 101]
  
•  including the corresponding material on the lecture slides/notes
  
• Section 3.5: 6, 7 - 12
• Section 4.3: 6 [harder problem, but doable]
• Note: there was a typo on this assignment: originally 4.4 #6, instead of 4.3 #6
• Note: Students in 520 need to turn in their assignments in LaTeX.
• Exam II: Friday, March 27

Assignment 9--Due Wednesday, April 1:

• Quiz (420): No quiz in recitation on Monday, March 30: Topics: none
  
•  including the corresponding material on the lecture slides/notes
  
• Section 3.7: 2 - 5, 8
• Section 4.3: 2 (we did Lagrange interpolation in section 3.5)

Assignment 10--Due Wednesday, April 8:

• Quiz (420): Quiz in recitation on Monday, April 6: Topics: 3.7, 4.1 - 4.4 (through Corollary 2 on p 129)
  
•  including the corresponding material on the lecture slides/notes
  
• Section 4.2: 1, 3
• Section 4.2: 6 - 8
• Section 4.3: 1, 3 (We covered Lagrange interpolation in Section 3.5)
• Section 4.4: 1, 2b

Assignment 11--Due Wednesday, April 15:

• Quiz (420): Quiz in recitation on Monday, April 13 Topics: 4.4 - 5.2
  
•  including the corresponding material on the lecture slides/notes
  
• Section 4.4: 3, 4, 6
• Section 4.5: 2, 3
• Section 5.2: 1, 3, 9, 12

Assignment 12--Due Wednesday, April 22:

• Quiz (420): Quiz in recitation on Monday, April 19 Topics: 5.3 (Statement of Theorem 2; Theorem 3 and proof); 5.4, 6.1, 6.2
  
•  including the corresponding material on the lecture slides/notes
  
• Section 5.3: 6, 7, 10
• Section 5.4: 3, 5, 8
• Section 6.2: 5, 8, 9, 13 [note #13 added to assignment]

Assignment 13--Due Wednesday, April 29:

• Quiz (420): Quiz in recitation on Monday, April 27 Topics: 6.3, 6.4 to bottom of page 200
  
•  including the corresponding material on the lecture slides/notes
• including Cayley-Hamilton Theorem
  
• Section 6.3: 3 - 7
• Section 6.4: 1, 3, 8
• Note: #5, on the previous tentative list, will be due next assignment

Assignment 14--Due Wednesday, May 6:

• Quiz (420): No quiz in recitation on Monday, May 4
  
• Section 6.4: 5, 10 [10 was added to the assignment]
• Section 6.6: 1, 2

Exam I

• When: Friday, Feb 27 at 11:00-11:50 AM
• Where: Math 150
• Covers: Sections 1.1 -  3.1
• including the corresponding material on the lecture slides/notes
• Format: 1 or 2 statements/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• Review Session: Wednesday, February

Exam II

• When: Friday, March 27 at 11:00-11:50 AM
• Where: Math 150
• Covers: Sections 3.2 - 3.5
• including the corresponding material on the lecture slides/notes
• Format: 1 or 2 statements/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• Review Session: TBA

Exam III

• When: Friday, May 1 at 11:00-11:50 AM
• Where: Math 150
• Covers: Sections 3.7, 4.1 - 5.2, 5.3 (Statement of Theorem 2; Theorem 3 and proof); 5.4, 6.1 - 6.4 to bottom of page 200
• including the corresponding material on the lecture slides/notes
• including the Cayley-Hamilton Theorem
• Format: 1 or 2 statements/definitions; 3 or 4 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed
• Review Session: Wednesday, April 29, TBA