## SPRING 2021

LINEAR ALGEBRA AND APPLICATIONS (4) Matrix algebra and solutions of systems of linear equations, matrix inversion, determinants. Vector spaces, linear dependence, basis and dimension, subspaces. Inner products, Gram-Schmidt process. Linear transformations, matrices of a linear transformation. Eigenvalues and eigenvectors. Applications. Constructing and writing mathematical proofs. A transition between beginning calculus courses and upper-level mathematics courses.
PRQ: MATH 232, Calculus III

TEXT: Elementary Linear Algebra with Applications (ninth edition) by Bernard Kolman and David R. Hill. (2007 or 2018 copyright)

SYLLABUS: The course will cover most of Chapters 1-7 of the text.

COURSE OBJECTIVES: Students will develop computational skills in working with linear transformations and the matrices used to represent them. However, more of the course will focus on non-computational issues such as reasoning and constructing proofs. This course is intended as a transition between the beginning calculus courses and upper level courses in mathematics.

CALCULATORS: This course is not focused on numerical computation. Students may wish to use calculators or computers as a study aid, but no electronic devices of any kind will be allowed on exams. See how a calculator can give you a completely wrong answer. Techniques from numerical linear algebra are covered in a subsequent course, MATH 434.

FINAL EXAM: The final exam will be a comprehensive, departmental examination. It is scheduled as a mass exam, on Thursday, April 29, 8:00-9:50 AM. All sections of this course will take the same final exam at the same time.

WITHDRAWAL: The last day for undergraduates to withdraw from a full-session course is Friday, March 19, 2021.

LECTURES AND EXAMS: This is the tentative schedule for lectures and exams.

```
Week of      Sections
1/11     1.1, 1.2, 1.3

1/18     MLK Day, 1.4, 1.5, 2.1

1/25     2.2, 2.3, 3.1, 3.2

2/1      3.3, 3.4, 3.5, 4.2

2/8      4.3, Day off, Exam 1

2/15     4.4, 4.5

2/22     4.6, 4.7

3/1      4.8, 4.9

3/8      5.1, 5.3, Day off

3/15     Exam 2, 5.4, 5.5

3/22     6.1

3/29     6.2

4/5      6.3, 6.5, 7.1

4/12     7.2, Exam 3

4/19     7.3, Review

FINAL EXAM: Thursday, April 29, 8:00-9:50 AM.
```

HOMEWORK PROBLEMS: These are the suggested homework problems. The assigned homework problems may vary by section.

```   Section|Problems

1.1        2  3  5  10 11 14 15 34
1.2        5  8  13 19
1.3        5  7  14 23 28 31 33 36 43 49
1.4        3  5  10 22 32 36
1.5        3  11 17 21 22 24 32 33 35 36 40 51

2.1        1  3  5  8
2.2        1  5  7  14 23 31
2.3        2  5  8  12 13 17 24 29

3.1        2  3  5  8  12
3.2        1  8  9  10 14 15 23 24 30 32
3.3        1  4  5  12
3.4        2  4  14
3.5        3  5

4.2        1  3  6  23 24 25
4.3        1  4  5  13 15 17 19 23 24
4.4        1  3  4  8  12 13
4.5        1  2  3  12 13 23 24
4.6        8  10 20 28 30 32 44 47
4.7        4  9
4.8        6  7  10 15 23 24 26 29 37 42
4.9        2  7  14 18 34 35 45

5.1        6  10 18 25
5.3        7  14 17 19 20 30 31 41
5.4        2  5  11 15 21 23
5.5        2  7  9  11 15 19

6.1        2  4  8  9  12 13 16 17 32 34
6.2        1  8  10 12 16 20 25
6.3        1  8  9  22
6.5        1  3  6  7  11

7.1        2  7  12 17 21
7.2        6  11 18 19 26
7.3        1  2  3  4  8  11 16 19
```

REVIEW: Chapter Summaries of the textbook.
Previous final exams: Fall 2002, Fall 2004, Fall 2008, Spring 2011, Spring 2016, Fall 2009 with solutions.

ACADEMIC INTEGRITY STATEMENT: Good academic work must be based on honesty. The attempt of any student to present as his or her own work that which he or she has not produced is regarded by the faculty and administration as a serious offense. Students are considered to have cheated if they copy the work of another during an examination or turn in a paper or an assignment written, in whole or in part, by someone else. Students are guilty of plagiarism, intentional or not, if they copy material from books, magazines, or other sources without identifying and acknowledging those sources or if they paraphrase ideas from such sources without acknowledging them. Students guilty of, or assisting others in, either cheating or plagiarism on an assignment, quiz, or examination may receive grade of F for the course involved and may be suspended or dismissed from the university.

DRC STATEMENT: If you need an accommodation for this class, please contact the Disability Resource Center as soon as possible. The DRC coordinates accommodations for students with disabilities. It is located in Suite 180 of the Campus Life Building, and can be reached at 815-753-1303 or drc@niu.edu.