MATH 3330 HOMEWORK (Fall 2018)

MATH 3330 HOMEWORK (Fall 2018)

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Book = Linear Algebra with Applications, 5th Ed, O. Bretscher, Prentice Hall.

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Homework will not be collected.
There might be more than one correct answer for any given question.
Dates indicate homework assigned in lecture on that date. Dates for future assignments are tentative, and subject to change. (However, it will be similar to the homework posted here.)
On some dates, the questions are in a nonincreasing order; that is the order recommended by your instructor and is usually chosen to match the order in which the material was presented in class.
Any optional exercises are for those students who wish to explore some of the ideas in more depth – those questions are NOT game for the tests.
Skimming through the main ideas in a section shortly before that section is covered in class should help you understand the lecture -- try it!
Also, see the links to practice quizzes/tests on my website.
Recall that our test dates are: Sept 17, Sept 26, Oct 17, Nov 12, Dec 7.
LAST REVISION: 11/06/18.

08/22/18

Attendance will be recorded, starting today.
Read course syllabus carefully. Make a note of the test dates in your calendar. Review course website and repeat frequently during the semester.
Read https://vancliff.utasites.cloud/T/study.pdf and read https://www.jeffreybennett.com/pdf/How_to_Succeed_general.pdf for ideas on how to study most effectively.

Read lecture notes (meaning the notes you should have taken during class) & Sec 1.1 &
do Sec 1.1: 2, 11-13, 16, 17. Try some practice quizzes.

08/27/18

Read lecture notes & do Sec 1.1: 19, 22 (note: Emile is a male name and Gertrude is a female name), 26, 31, 33,38, 45, 46, 50.
Read lecture notes & Sec 1.2. Do Sec 1.2: 1-4, 6, 8, 18, 21, 26, 27, 31, 43, 47, 48, 63.
Try some practice quizzes.

08/29/18

The following results are restatements of some of the results in Sec 1.3 and will be assumed in all future lectures.

Theorem L1

If we have m linear equations in n variables, then the coefficient matrix A has m rows and n columns (size m by n), and
(a) rank(A) ≤ m and rank(A) ≤ n, and the number of free variables = (total number of variables) – rank(A);
(b) if rank(A) = m, then the system is consistent;
(c) if rank(A) = n, then the system has at most 1 solution (could be none);
(d) if rank(A) < n, then the system has either has either no solution or infinitely many.
Reasoning: 1^st part of (a) observed in class today by a student and is to do with definition of rref(A); 2^nd part of (a) is owing to the free variables coming from columns of rref of coefficient matrix that do not contain a pivot, so the number of free variables is given by the total number of columns – the total number of pivots and hence equals the total number of variables – rank(A). The hypothesis in (b) means that every row of the rref of the coefficient matrix has a pivot and hence the equation 0 =1 cannot occur. The hypothesis in (c) means that every column of the rref of the coefficient matrix has a pivot and hence there are no free variables, so the system has a finite number of solutions or none, so a unique solution or none. The hypothesis in (d) means that at least one column of the rref of the coefficient matrix does not have a pivot in it and so the system has 1 or more free variables, and so the system has either an infinite number of solutions or is inconsistent.

Theorem L2

A linear system with fewer equations than variables has either no solution or infinitely many.
Reasoning: Hypothesis implies that m < n in Theorem L1, so Theorem L1(a) implies that rank(A) ≤ m , but m < n , and rank(A) < n, so use (d) of Theorem L1.

Theorem L3

Suppose m = n in Theorem L1. If rank(A) < n, then there is either no solution or infinitely many. However, if rank(A) = n, then the system has a unique solution.
Reasoning: rank(A) < n implies use (d) of Theorem L1. rank(A) = n implies rank(A) = n = m, so use (b) and (c) of Theorem L1.

Theorem L4

If m = n in Theorem L1, then the linear system has a unique solution if and only if rank(A) = n.
Reasoning: This is a restatement of Theorem L3.

Read lecture notes & Sec 1.3 & do: 1-7, 9-20.       Try some  practice quizzes.

By this time, you have seen quite a few theorems. It is best NOT to memorize the theorems, but to do enough of the homework that the results of the theorems become known to you, though perhaps with different wording or using pictures.

09/03/18

UTA Holiday (Labor Day): no lecture.

09/05/18

Read lecture notes & Sec 1.3 & do: 5-7, 9, 25, 57-59.
Do pages 38-40 (true/false questions): 1-11, 13, 14, 17, 18, 29, 34, 39, 43. 
Try some practice quizzes. I'll stop writing this, but it goes without saying on all the assignments, through end of semester.

09/10/18

Read lecture notes & Sec 2.1 (in particular, recall that linear transformation was defined differently in lecture; more closely aligned with Def 4.2.1 on page 178) & do Sec 2.1: 1-6, 35, 57(a)(b), 8-12, 14, 15, 57(c).

The Quiz will be 1 week from today; it will cover Secs 1.1-1.3.
See Blackboard for an information sheet with practice questions for the quiz.
See Blackboard after 3:30 pm Sunday Sept 16 for answers to the multiple-choice practice questions.

09/12/18

Read lecture notes & pgs 58-60 & pgs 1-3 of this file & learn table on pg 70 & do Sec 2.2: 1, 2, 8, 9, 11.
Make a note of the new date for Test 3 (Nov 12).
Quiz on Monday; see Sept 10 above for details.

09/17/18

Quiz today; see Sept 10 above for details.
Read lecture notes & pgs 58-60 & pgs 4-5 of this file & learn table on pg 70 & do Sec 2.2: 26(a), 4, 30, 10, 27.
Read lecture notes & pgs 75-81 & do Sec 2.3: 1-5, 7, 10, 11, 35, 43, 44.
Look over the Quiz & its solutions posted on Blackboard to study for Test 1; use password ``math3330'' to open the pdf file.
(If you have trouble opening the pdf file, send an email to Dr. Vancliff about it.)

09/19/18

Read lecture notes & pgs 75-81 & do Sec 2.3: 20, 22, 26, 57, 58, 61.
Read lecture notes & Sec 2.4 & do: 1, 2, 16, 17, 37.
Do pages 107-109 (T/F): 1, 3, 7, 9-13, 15, 17, 25, 27, 28, 30, 35, 39, 47.

Test 1 will be 1 week from today; it will cover Secs 1.1-1.3, 2.1-2.3.
Look over the Quiz & its solutions posted on Blackboard to study for Test 1; use password ``math3330'' to open the pdf file.
See Blackboard for an information sheet with practice questions for Test 1.
See Blackboard after 3:30 pm Tuesday Sept 25 for answers to the multiple-choice practice questions for Test 1.

09/24/18

Read lecture notes & Sec 2.4 & do: 5, 6, 10, 13, 19, 29, 30, 35, 40.
Do pages 107-109 (T/F): 5, 18, 21, 22, 34.
Test 1 on Wednesday; see Sept 19 above for details.

09/26/18

Test 1 today; see Sept 19 above for details.
Read lecture notes & Sec 3.1 & do: 14-16, 19, 22, 17, 30, 32.

10/01/18

Read lecture notes & Sec 3.1 & do: 1-8, 12, 33, 34, 44.
Go over the solutions to Test 1 posted on Blackboard; use password ``math3330'' to open the pdf file.
(If you have trouble opening the pdf file, send an email to Dr. Vancliff about it.)

10/03/18

Read lecture notes & Sec 3.2 & do Sec 3.2: 1-3, 5, 34, 48, 49, 8-13.

10/08/18

Read lecture notes & Sec 3.2 & learn Theorem 3.2.8 on pg 128 & do Sec 3.2: 14-16, 21, 24, 43, 27, 28.

10/10/18

Read lecture notes & Sec 3.3 (especially pg 142) & learn Summary 3.3.10 on pg 142.
Do Sec 3.3: 31, 26, 29, 30, 36, 16, 17, 19-21, 12, 13, 38, 39, 28, 82, 83.

Test 2 will be 1 week from today; it will cover Secs 1.1-3.3.
See Blackboard for an information sheet, with practice questions for Test 2.
See Blackboard after 3:30 pm Tues Oct 16 for answers to the multiple-choice practice questions for Test 2.

10/15/18

Read lecture notes & Sec 3.4, especially pgs 155-7.
Do Sec 3.4: 3, 7, 12, 16, 17, 43-45, 48,, 19, 21, 27,, 59, 60.
Do pages 163-5 (T/F): 1-7, 9, 13, 14, 16, 18, 20, 28, 33, 35,, 11.
Test 2 on Wednesday; see Oct 10 above for details.

10/17/18

Test 2 today; see Oct 10 above for details.
Read lecture notes & pgs 166-174.
Do Sec 4.1: 1-4 (see Example 12 for the notation & see Example 16).

10/22/18

Read lecture notes & pgs 166-174 & do Sec 4.1: 7, 8, 20-22, 25, 26, 29, 30, 33.
Go over the solutions to Test 2 posted on Blackboard; use password ``math3330'' to open the pdf file.
(If you have trouble opening the pdf file, send an email to Dr. Vancliff about it.)
Read through the suggestions of study techniques from Aug 22 above and see which one(s) might work for you.

10/24/18

Read lecture notes & Sec 4.2 (especially Example 6 & table on pg 183).
Do Sec 4.2: 1, 3, 7, 9, 11, 17, 19, 22, 23.

10/29/18

Read lecture notes & do Sec 4.2: 42-44, 60.
Read lecture notes & do Sec 4.3: 21, 23, 24, 15, 16, 29, 32, 33.
Do pages 199-201 (T/F): 2-6, 8, 12, 13, 18, 24, 27, 37, 51.

10/31/18

Read lecture notes & do Sec 4.3: 46, 48, 57, 61b, 60ab.
Do pages 199-201 (T/F): 35.
Read pgs 202-204 & lecture notes & do
Sec 5.1: 1-3, 10, 16, 29, 15, 17 &
Sec 5.2: 1, 5, 7, 33, 35.

11/05/18

Read pgs 225-231 & lecture notes & do Sec 5.3: 1-9, 35-37, 13-18, 21-24, 38, 52, 57, 61.
Do page 263-4 (T/F): 2, 3, 5, 7, 8, 12, 13, 18, 23-25, 37.

Test 3 will be 1 week from today; it will cover Secs 1.1-5.3.
See Blackboard for an information sheet, with practice questions for Test 3.
See Blackboard after 1:30 pm Sunday Nov 11 for answers to the multiple-choice practice questions for Test 3.

11/07/18

Read lecture notes & do Sec 6.1: 1, 2, 5, 6, 9, 10, 12, 14, 15, 17, 19, 21, 22, 25, 29, 32-34, 45.
Read lecture notes & do Sec 6.2: 1, 5, 6, 11-16, 35, 38-40, 45, 46, 17, 27.
Read pgs 300.5-302, 304-304.5. Do Sec 6.3: 22-24, 31, 33.
(This material from Sec 6.3 was not covered in class, but is covered on the homework.)
Do page 308-9 (T/F): 1, 3, 4, 8, 11, 12, 17, 20, 46.
Test 3 on Monday; see Nov 5 above for details.

11/12/18

Test 3 today; see Nov 5 above for details.

11/14/18

Read Sec 7.1 & lecture notes & learn Summary 7.1.5 on pg 315 & Theorem 7.1.3 on pgs 312-3.
Theorem L49 from lecture = Theorem 7.1.3 in book.
Do Sec 7.1: 25, 27, 29, 24, 26, 28, 67, 69,, 38, 13, 8, 9, 1-5, 34, 46, 47, 51.

11/19/18

Read lecture notes & pgs 327-328, 331, 335 & do Sec 7.2: 9-12, 15, 29, 32, 45.
Go over the solutions to Test 3 posted on Blackboard; use password ``math3330'' to open the pdf file.

11/21/18

No classes nor office hours today; UTA offices open.
See the academic schedule at https://www.uta.edu/uta/acadcal.php

11/26/18

Read lecture notes and Sec 7.3. Learn Theorem 7.3.7 on pg 344.
Do Sec 7.3: 5, 6, 9, 10, 13, 15, 17, 18, 35, 36.
Read lecture notes & pgs 352-4. Do Sec 7.4: 5, 11, 49, 50, 48, 51, 39, 40.
Do pgs 382-4(T/F): 3, 6-8, 19, 29, 31, 45, 53.

11/28/18

Read Sec 8.1 & lecture notes. Do Sec 8.1: 5, 6, 9, 10, 14, 21, 22, 24, 31.

12/03/18

No new homework; today's lecture will be a chance for you to ask questions.
Please remember to complete online the student feedback survey by 11 pm on Tues Dec 4  -- check your mymav e-mail for the link.
I appreciate the feedback (e.g., quality of website, study sheets, etc?); thank you!

I will have my usual office hours through Dec 3 inclusive, and I will also have additional office hours as noted below.

12/05/18

1:40-3:50 PM and 4:40-6:30 PM: office hours in PKH 462.

12/07/18

FINAL TEST today, starting at 5:30 pm; see Blackboard for an information sheet, with practice questions.
See Blackboard after 4:00 pm Wed Dec 5 for answers to the multiple-choice practice questions.

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