Revised 05/09/17 10:55 AM
MTH 420/520--A 2nd Course in Linear Algebra--Homework Assignments
Homework: due Monday in lecture
Quiz(420 only): Friday in recitation
Exams:
- Exam I: Wednesday, March 8 completed
- Exam II: Wednesday, April 12 completed
- Exam III: Friday, May 5 completed
- Final Exam: Monday, May 15, 2017, 11:45 AM - 2:45 PM
in Math 150
Office Hours:
- 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.
Week of May 8:
- Quiz (420): Quiz on Friday, May 12. Topics: 6.4, 6.6
- One statement or definition
- One problem or proof
- Assignment 14:
- Section 6.6: 1, 2, 3, 5
- Section 6.7: 1
Final Exam
- When: Monday, May 15, 11:45 AM - 2:45 PM
- Where: Math 150
- Covers: Sections 1.1 - 3.5, 3.6*, 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)
- * "as covered in lecture"
- annihilator/pre-annihilator and relationships between them
- for 5.3: Statement of Theorem 2; Theorem 3 and proof
- including the
corresponding material on the lecture slides/notes
- including
the Cayley-Hamilton Theorem
- 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 (tentative list of upcoming assignments):
Week of January 30:
- Recitation for 420: Recitation
may meet Friday, February
3, at 8:00 AM in Math 150
- Read: Sections: 1.1 - 1.5
- Assignment 1:
- Due Monday, February 6
- 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)
- 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]
Week of February 6:
- Quiz (420): Quiz I on Friday, February 10 in
recitation. Topics: Chapter 1
- One statement or definition
- One problem or proof
- Assignment 2:
- Due Monday, February 13
- 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--assignment deleted.
Will be due next Monday.
Week of February 13:
- Quiz (420): Quiz II on Friday, February 17 in
recitation. Topics: 2.1 - 2.3 (through Corollary 2 on page 46)
- One statement or definition
- One problem or proof
- Assignment 3:
- Due Monday, February 20
- Section 2.2: [1 - 2],
3, 5, 7, 9
- Problem 3 has a misprint; should be R^4 not R^5
- 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)
Week of February 20:
- Quiz (420): Quiz III on Friday, February 24 in
recitation. Topics: 2.3 - 3.1 (through (b) on the middle of p. 71)
- One statement or definition
- One problem or proof
- Assignment 4:
- Section 2.4: 1, 2, 4, 6
- 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
Week of February 27:
- Quiz (420): Quiz IV on Friday, March 3 in recitation.
Topics: 3.1
- One statement or definition
- One problem or proof
- Exam I: Wednesday, March 8 (see details below)
- Assignment 5:
- 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
Week of March 6:
- Quiz (420): No Quiz on Friday, March 10 in
recitation. Topics: None
- Assignment 6:
- Section 3.3: 2, 3, 5, 7
- Section 3.4: 2, 5, 10, 12
Week of March 13:
- Quiz (420): Quiz on Friday, March 17 in recitation.
Topics: 3.2 - 3.5 (up to but not including Example 22 on p 100)
- One statement or definition
- One problem or proof
- Assignment 7:
- 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 4.3: 6 [harder
problem, but doable]
Week of March 27:
- Quiz (420): Quiz on Friday, March 31 in recitation.
Topics: 3.5, 3.6 from class (all the material on annihilators and
pre-annihilators in the lecture notes)
- One statement or definition
- One problem or proof
- Assignment 8:
- Section 3.5: 6 - 9
- Section 3.7: 2, 3
Week of April 3:
- Quiz (420): Quiz on Friday, April 7 in recitation.
Topics: 3.7, 4.1, 4.2
- One statement or definition
- One problem or proof
- Assignment 9:
- Section 3.7: 4, 5, 8
- Section 4.3: 2 (We covered
Lagrange interpolation in Section 3.5)
- Section 4.2: 1, 3
Week of April 10:
- Quiz (420): No quiz on Friday, April 14 in
recitation. Topics: None
- One statement or definition
- One problem or proof
- Assignment 10:
- Section 4.2: 6 - 8
- Section 4.3: [1], 3 (We
covered Lagrange interpolation in Section 3.5)
- 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
Week of April 17:
- Quiz (420): Quiz on Friday, April 21 in recitation.
Topics: 4.4, 4.5, 5.1, 5.2, 5.3 (Thm 3 only), 5.4
- One statement or definition
- One problem or proof
- Assignment 11:
- 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
- Section 5.3: 6, 7, 10
- Section 5.4: 3, 5, 8
Week of April 24:
- Quiz (420): Quiz on Friday, April 28 in recitation.
Topics: 6.2, 6.3, beginning of 6.4 (up to bottom of page 199)
- One statement or definition
- One problem or proof
- Assignment 12:
- Section 6.2: 5, 8, 9, 13
- Section 6.3: 3 - 7
- Section 6.4: 1, 3, 8
(revised: #2 postponed to next assignment)
- Exam III: Friday, May 5
Week of May 1:
- Quiz (420): No quiz on Friday, May 5. Last quiz on
Friday, May 12. Topics: TBA
- One statement or definition
- One problem or proof
- Assignment 13:
- Section 6.4: 2
- Section 6.4: 5, 10
- Section 6.4: 12 (added to
Assignment 13)
Exam I
- When: Wednesday, March 8 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:
- 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: April 12 at 11:00 - 11:50 AM
- Where: Math 150
- Covers: Sections 3.2 - 4.3 (just Lagrange
interpolation in 4.3)
- including the
corresponding material on the lecture slides/notes
- we skipped the double dual
in 3.6; the rest of 3.6 is in the 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, May 5 at 11:00 - 11:50 AM
- Where: Math 150
- Covers: Sections 4.4, 4.5, 5.1 - 5.4, 6.2, 6.3,
beginning of 6.4 (up to bottom of page 199)
- 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:
- 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