MTH 420/520--Abstract Linear Algebra--Homework Assignments

Quiz(420 only): Wednesdays in recitation

Exams:

• Exam I: Wednesday, February 27 completed
• Exam II: Wednesday, March 27 completed
• Exam III: Friday, April 26 completed
• Final Exam: Monday, May 13, 2019, 11:45 AM - 2:45 PM in Math 150

• TBA, 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.

Week of May 6

• Read: Sections: 3.7
  
• Assignment (these are possible exam questions, not to be turned in):
• Section 3.7: 1 -3
• Quiz for 420: Quiz this week on Wednesday, May 8
• Topics: 3.5, 3.6 (skip double dual itself), 3.7
• Dual space, dual basis, annihilator, pre-annihilator, results on dimension of annihilator and pre-annihilator
• transpose of a linear transformation

Final Exam

• When: Monday, May 13, 11:45 AM - 2:45 PM
• Where: Math 150
• Covers: Sections 1.1 - 3.5, 3.6*, 3.7
• * "as covered in lecture" (not including the double dual itself)
• annihilator/pre-annihilator and relationships between them
• including the corresponding material on the lecture slides/notes
• 420 Format: 1 to 3 definitions or statements of result, 6 - 10 problems/proofs
• proofs from the book or lecture, or pieces of proofs, may well be on the exam
• 520 Format: 8 to 12 problems/definitions/proofs/statement of theorems
• Seating will be assigned
• No alphanumeric/programmable/graphing calculators allowed

Coming Attractions (very tentative list of upcoming assignments):

• Summer

Week of January 28: School was cancelled on Wednesday, January  30. No recitation, no quiz, no homework

• Recitation for 420: Recitation will meet Wednesday, January 30, at 8:00 AM in Math 150 [Note change in room to 150]
• Read: Sections: 1.1 - 1.5
• Assignment 1:
• Due Monday, February 4
• problems listed for an assignment are to be handed on the due date in class. 
• You may type them in LaTeX (required for graduate students)
• TBA
• Quiz for 420: Quiz this week on Wednesday, January 30
• Topics: Review of Matrix Multiplication, Linear independence/dependence, inverse of a matrix
• Look at your notes from Linear Algebra or look up these topics on the internet

Week of February 4:

• 1st Recitation for 420: Wednesday, February 6th, at 8:00 AM in Math 150
• Read: Sections: 1.1 - 1.5
• Review on you own: Matrix Multiplication, Linear independence/dependence, inverse of a matrix
• these topics are easily found on the internet or in any basic linear algebra book
  
• Assignment 1:
• Due Monday, February 11
• problems listed for an assignment are to be handed on the due date in class.
• You may type them in LaTeX (required for graduate students)
• Section 1.2:  1 - 4, 6, 7 Problems in brackets should be done, but not turned in
• Note: problems 1 and 6 were added to the original assignment
• Quiz for 420: Quiz this week on Wednesday, February 6
• Format:
• One statement or definition
• One problem or proof
• Topics:
• Matrix Multiplication and linear independence/dependence
• Section 1.2

Week of February 11:

• Read: Sections: 1.6, 2.1
  
• Assignment 2:
• Due Monday, February 18
• you may type them in LaTeX (required for graduate students)
• Section 1.3:  3, [5], 7
• Section 1.4:  1, 4, 8, 10 a hard problem
• Section 1.5:  3, [6]
• Quiz for 420: Quiz this week on Wednesday, February 13
• Format:
• One statement or definition
• One problem or proof
• Topics: 1.3 - 1.5

Week of February 18:

• Read: Sections: 2.4 - 2.5
  
• Assignment 3:
• Due Monday, February 25
• Section 1.5:   4,  8 (a hard problem)
• 4 added to assignment
• See UBLearns>CourseDocuments>HW for a hint for 8
• Section 1.6: 1, 5 - 7, 10, [11]. Look at 12 (extremely hard problem)
• Quiz for 420: Quiz this week on Wednesday, February 20
• Format:
• One statement or definition
• One problem or proof
• Topics: 1.4 - 1.6

Week of February 25:

• Read: Sections: 2.4 - 2.5
  
• Assignment 4:
• Due Monday, March 4
• Section 2.1: 4, 6, [7]
• Section 2.2: [1 - 2],  3, 5, 7,  9
• Quiz for 420: No Quiz this week on Wednesday, February 27

Week of March 4:

• Read: Sections: 2.4 - 2.6
  
• Assignment 5:
• Due Monday, March 11
• Section 2.3:  [1],  4, 9 - 11, 13, 14 (a harder, but still doable problem)
• Note: (Problem 13 references Exercise 5 in Section 1.2, not 1.1)
• Quiz for 420: Quiz this week on Wednesday, March 6
• Topics: 2.2, 2.3 (through Theorem 4)

Week of March 11:

• Read: Sections: 2.4 - 2.6
  
• Assignment 6:
• Due Monday, March 25
• Section 2.3: 2, 7
• Section 2.4: 2, 4, 6
• Quiz for 420: Quiz this week on Wednesday, March 13
• Topics: 2.2, 2.3 (through Theorem 6--including finding the spanning set for W_1 + W_2)

Week of March 25

• Read: Sections: 3.1 - 3.2
  
• Assignment 7:
• Due Monday, April 1
• Section 2.6: 1, [2], 3, 5
• For Problem 1:  Theorem 4 is on p 44
• Note: Example 22 in Section 2.6 will be posted to UBLearns>Course Documents>Matrix Manipulation
• Section 3.1: 4, 5, 10
• Quiz for 420: no quiz this week on Wednesday, March 27

Week of April 1 

• Read: Sections: 3.1 - 3.5
  
• Assignment 8:
• Due Monday, April 8
• Section 3.1: 2, 8, 12
• Note: The example for problem 12 should be in the context of a general vector space of dim n even over a field F
• Section 3.2: 3 - 6, 8
• Section 3.2: 10, 11
• Quiz for 420: Quiz this week on Wednesday, April 3
• Topics: Linear Transformations, including range and kernel, Rank-Nullity Theorem

Week of April 8 

• Read: Sections: 3.1 - 3.5
  
• Assignment 9:
• Due Monday, April 15
• Section 3.3: 2, 3, 5, 7
• Quiz for 420: Quiz this week on Wednesday, April 10
• Topics:
• Linear Transformations, including range and kernel, Rank-Nullity Theorem
• 1 - 1, onto, invertibility, nonsingular/singular, linearity of inverse

Week of April 15

• Read: Sections: 3.5 - 3.7
  
• Assignment 10:
• Due Monday, April 22
• Section 3.4: 2, 5, 10, 12
• Quiz for 420: Quiz this week on Wednesday, April 17
• Topics
• isomorphisms
• matrix of linear transformation
• change of basis
• linear functionals
• Exam III: Friday, April 26

Week of April 22

• Read: Sections: 3.5 - 3.7
  
• Assignment 10:
• Due Wednesday, May 1
  
• 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.
• TBA
• Quiz for 420: No Quiz this week on Wednesday, April 24

Week of April 29

• Read: Sections: 3.6
  
• Assignment 11:
• Due Monday, May 6
  
• Section 3.5: 6- 9, 11,12
• Quiz for 420: Quiz this week on Wednesday, May 1
• Topics: 3.5
• Dual space, dual basis, annihilator, pre-annihilator, results on dimension of annihilator and pre-annihilator

Exam I

• When: Wednesday, February 27 at 11:00-11:50 AM
• Where: Math 150
• Covers: Sections 1.1 -  2.1
• including the corresponding material on the lecture slides/notes
• Format:
• 420: 1 or 2 statements/definitions; 3 or 4 problems/proofs
• 520: 4 or 5 problems/definitions/proofs/statement of theorems
• 420/520: 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: Wednesday, March 27 at 11:00-11:50 AM
• Where: Math 150
• Covers: Chapter 2
• including the corresponding material on the lecture slides/notes
• Format:
• 420: 1 or 2 statements/definitions; 3 or 4 problems/proofs
• 520: 4 or 5 problems/definitions/proofs/statement of theorems
• 420/520: 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: Friday, April 26 at 11:00-11:50 AM
• Where: Math 150
• Covers: Chapter 3, up to and including Section 3.5 Example 22 on page 100
• including the corresponding material on the lecture slides/notes
• Format:
• 420: 1 or 2 statements/definitions; 3 or 4 problems/proofs
• 520: 4 or 5 problems/definitions/proofs/statement of theorems
• 420/520: 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