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

Exams:

• Exam I: Monday, February 29 completed
  
• Exam II: Monday, March 28 completed
• Exam III: Monday, April 25 completed
• Final Exam: Monday, May 9 in Baldy 101

• Monday 1:30 - 2:20, Wednesday 12:30 - 1:20, and by appointment

Textbook: 

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

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

Assignment 12--Due Wednesday, May 4:

• Quiz (420): Quiz on Monday, May 2 in recitation.Topics: 6.3, 6.4
  
• including the corresponding material on the lecture slides/notes
• One statement or definition
• One problem or proof
• Section 6.4: 5, 10
• Section 6.6: 1, 2

Final Exam

• When: Monday, May 9, 11:45 AM - 2:45 PM
• Where: Baldy 101
• Covers: Sections 1.1 - 3.5, 3.7, 4.1, 4.2, 4.4, 4.5, 5.1 - 5.4, 6.1 - 6.4, 6.6 (to bottom of page 211)
• for 5.3: Statement of Theorem 2; Theorem 3 and proof; skip rest of 5.3
  
• 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

Coming Attractions (tentative list of upcoming assignments):

• Final Exam

Assignment 1--Due Wednesday, February 3:

• Recitation for 420: Recitation will meet  Monday, January 25, at 8:00 AM in Math 150
• Quiz (420): Quiz I on Monday, February 1 in recitation. Topics: 1.1 - 1.5
• One statement or definition
• One problem or proof
  
• Section 1.2:  [1], 2 - 4, 7 Problems in brackets should be done, but not turned in
• Section 1.3:  3, [5]
• Section 1.4:  1, 4, 8, 10
• Section 1.5:  3, [6]
• 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 10:

• Quiz (420): Quiz II on Monday, February 8 in recitation. Topics: 1.6, 2.1, 2.2
  
• One statement or definition
• One problem or proof
  
• Section 1.5: 4, 8
• 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 3--Due Wednesday, February 17:

• Quiz (420): Quiz III on Monday, February 15 in recitation. Topics: 2.3, 2.4
  
• One statement or definition
• One problem or proof
  
• 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 4--Due Wednesday, February 24:

• Quiz (420): Quiz IV on Monday, February 22 in recitation. Topics: 2.5, 2.6, 3.1
  
• One statement or definition
• One problem or proof
  
• 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: The example for problem 12 should be in the context of a general vector space of dim n over a field F

Assignment 5--Due Wednesday, March 9:

• Quiz (420): Quiz V on Monday, March 7 in recitation. Topics: 3.2, 3.3
  
• One statement or definition
• One problem or proof
  
• Section 3.2: 3 - 6, 8
• Section 3.2: 10, 11
• Section 3.3: 2, 3, 5, 7

Assignment 6--Due Wednesday, March 23:

• Quiz (420): Quiz VI on Monday, March 21 in recitation. Topics: 3.4, 3.5
  
• One statement or definition
• One problem or proof
  
• 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.
• Section 3.5: 6 - 9

Assignment 7--Due Wednesday, March 30:

• Quiz (420): No Quiz on Monday, March 28 in recitation.
  
• One statement or definition
• One problem or proof
  
• Section 4.3: 6 [harder problem, but doable]
• Section 3.7: 2 - 5, 8

Assignment 8--Due Wednesday, April 6:

• Quiz (420): Quiz on Monday, April 4 in recitation. Topics: 3.7, 4.1, 4.2
  
• One statement or definition
• One problem or proof
  
• Section 4.3: 2 (we did Lagrange interpolation in section 3.5)
• Section 4.2: 1, 3
• Section 4.2: 6 - 8
• Section 4.3: [1], 3 (We covered Lagrange interpolation in Section 3.5)

Assignment 9--Due Wednesday, April 13:

• Quiz (420): Quiz on Monday, April 11 in recitation. Topics: 4.4, 4.5, 5.2
• including the corresponding material on the lecture slides/notes
• One statement or definition
• One problem or proof
• Skip the proof of existence and skip permutations and the proof of uniqueness
  
• Section 4.4: 1, 2b, 3, 4, 6
• Ideal generated by f_1, ..., f_n = {g_1 f_1 + ... + g_n f_n | g_i \in F[x]}; see example 6 on p 131
• Section 4.5: 2, 3
• (Typo in Problem 7--not an assigned problem--should refer to Exercise 6 not to Exercise 7)
• Section 5.2: 1, 3, 9, 12

Assignment 10--Due Wednesday, April 20:

• Quiz (420): Quiz on Monday, April 18 in recitation. Topics: 5.3, 5.4, 6.2, 6.3 (up to where we get on Friday)
  
• including the corresponding material on the lecture slides/notes
• One statement or definition
• One problem or proof
• Skip the proof of existence and skip permutations and the proof of uniqueness
  
• Section 5.3: 6, 7, 10
• Section 5.4: 3, 5, 8
• Section 6.2: 5, 8, 9, 13
• Section 6.3: 3 - 7

Assignment 11--Due Wednesday, April 27:

• Quiz (420): No Quiz on Monday, April 25 in recitation.
  
• Section 6.4: 1 - 3, 8 (Note addition of 2 to the assignment)

Exam I

• When: Monday, Feb 29 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

Exam II

• When: Monday, March 28 at 11:00-11:50 AM
• Where: Math 150
• Covers: Sections 3.2 - 3.5
• including the corresponding material on the lecture slides/notes
• includes pre-annihilator and hyperplane material on 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

Exam III

• When: Monday, April 25 at 11:00-11:50 AM
• Where: Math 150
• Covers: Sections 3.7, 4.1, 4.2, 4.4, 4.5, 5.1 - 5.4, 6.2, 6.3
• including the corresponding material on the lecture slides/notes
• Skip the proof of existence of determinants and skip permutations and the proof of uniqueness
• 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