Math 2331, Section 24154 - Fall 2008

Linear Algebra

Classes: 10:00-11:30am TuTh, 634 SR1
Prerequisite: Credit for or concurrent enrollment in MATH 1432.
Course description
- Syllabus: see the department page of syllabi for the HTML or PDF versions
Instructor: Andrew Török
- Office: 672 PGH
- Phone: (713) 743-3478
- E-mail: see the home-page
- Office hours: see the home-page
Grader: Sukhlal Ramharack
Extra (free) help:
- Tutoring offered by the Math Dept: CASA, 222 Garrison Gym, http://www.casa.uh.edu/casa/ (look under Tutoring Center)
- Learning Support Services, 321 Social Work Bldg, phone (713) 743-5411, http://las.uh.edu/lss/ (see Tutoring; Math 2331 used to be Math 2431)

Examinations

The syllabus suggests that the three tests be given after Chapters 2, 4 and 6. We will follow this, with a possible exception for the third test.

Exam I: Oct. 2, Thursday
- The exam will cover the first two chapters.
- There is no problem involving MATLAB on the exam.
- Please bring your student I.D.
- It will be a closed book exam.
- No calculators.
- A list with review problems is here.
- Review: Thursday, Sep. 25. We will discuss the review problems, and any questions you might have.
- Approximate results:
  - 59 students took the test
  - average: 73/100
  - min, quartiles, max: 14, 63, 74, 83.5, 100 (i.e, there are about 25% of students in each of these four intervals).

Assignments

The problems below are from the textbook. Please write the solutions on separate pages (i.e., do not hand in a note-book), and STAPLE the pages together.

LATE homeworks will receive a 20% penalty. I should receive them during the class following the one when the HW was due.

Some of the problems have the answer or a hint in the textbook. If you have to hand in such a problem, you are welcome to use the hint but have to still write a complete solution.
For problems that require Matlab, you can either hand in the printed Matlab computations, or a hand written copy of them.

Problems marked with a star, *, are more difficult. Those marked with s are solved in the book (but not all solved problems are marked).

HOMEWORKS (M = use Matlab)
HW # Section HAND IN Solve only, do not hand in

1. (due Aug. 28) 1.1 6 1, 4, 5, 13* (a,b), 14*
1.2 6 (a,b), 16 2, 3, 5, 8
2. (due Sep. 4) 2.1 10, 11, 16, 18, 27 1, 2s, 3s, 17s, 19s
2.2 6, 11, 12, 19, 21 22
3. (due Sep. 9) 2.3 16, 17, 19, 20, 21, 23, 24 1s, 3s and 4, 12s, 18s, 25s, 27s
4. (due Sep. 18)
no penalty if
handed in on Tu, Sep. 23 2.4 rules for matrix operations
1, 6, 8, 14, 21 5, 9, 11, 13, 30, 36
2.5 3, 6, 13, 17, 25, 32 1, 4, 7, 12, 14, 26, 29, 33
Proof of [A B = I => B A = I for square matrices].
Done on Tuesday, Sep. 16:

how to solve A x = b if the A=LU factorization is known (see page 86 in the textbook)
apply this for the A=LU factorization computed last time and b=[1 2 3], b=[5 6 7]
another example: factor A=[1 1 1; 2 4 5; 3 9 6], solve A x = [1 2 3]
uniqueness of A=LU, A=L D U factorizations for A invertible (see problem 18s):

If either L or U has 1's on its diagonal, then the A=LU factorization is unique.

If both L and U have 1's on the diagonal, then the A=L D U factorization is unique.

began section 2.7: pages 96-97, without proofs
Done on Thursday, Sep. 18:

finished section 2.7

first exam after done with HW's from chapter 2; see review problems above

5. (due Thursday, Sep. 25) 2.6 5, 7, 11, 16 8, 18s, 32, 33, 34, 35 (Matlab later)
2.7 3, 11, 16 2s, 20s, 36, proof at bottom of page 109, 22s, 24s
6. (due Tuesday, Sep. 30) 3.1 10, 12, 13, 19, 26 5s, 11s, 15s, 16, 20s
7. (due Tuesday, Oct. 14) 3.2 7, 13, 15, 25 1, 2s, 3, 4s, 9, 21 (see 3D in sec. 3.3), 23 (this is a bit easier than 25), 24s
3.3 2, 12 6, 18s, 21s, 24s
3.4 I think the method described in class [solving directly from the (reduced) row echelon form and then separating the result] is better than the one in the book [setting the free variables to zeros or ones and then combining the results].
3, 11, 17, 20, 34 2s, 6s, 10, 12s, 22, 25s, 31, 33
Please staple the pages together and write your name clearly.

HOMEWORKS (M = use Matlab)
1. (due Aug. 28)	1.1	6	1, 4, 5, 13* (a,b), 14*
1.2	6 (a,b), 16	2, 3, 5, 8
2. (due Sep. 4)	2.1	10, 11, 16, 18, 27	1, 2s, 3s, 17s, 19s
2.2	6, 11, 12, 19, 21	22
3. (due Sep. 9)	2.3	16, 17, 19, 20, 21, 23, 24	1s, 3s and 4, 12s, 18s, 25s, 27s
4. (due Sep. 18) no penalty if handed in on Tu, Sep. 23	2.4	rules for matrix operations
1, 6, 8, 14, 21	5, 9, 11, 13, 30, 36
2.5	3, 6, 13, 17, 25, 32	1, 4, 7, 12, 14, 26, 29, 33
Proof of [A B = I => B A = I for square matrices].
Done on Tuesday, Sep. 16: how to solve A x = b if the A=LU factorization is known (see page 86 in the textbook) apply this for the A=LU factorization computed last time and b=[1 2 3], b=[5 6 7] another example: factor A=[1 1 1; 2 4 5; 3 9 6], solve A x = [1 2 3] uniqueness of A=LU, A=L D U factorizations for A invertible (see problem 18s): If either L or U has 1's on its diagonal, then the A=LU factorization is unique. If both L and U have 1's on the diagonal, then the A=L D U factorization is unique. began section 2.7: pages 96-97, without proofs Done on Thursday, Sep. 18: finished section 2.7 first exam after done with HW's from chapter 2; see review problems above
5. (due Thursday, Sep. 25)	2.6	5, 7, 11, 16	8, 18s, 32, 33, 34, 35 (Matlab later)
2.7	3, 11, 16	2s, 20s, 36, proof at bottom of page 109, 22s, 24s
6. (due Tuesday, Sep. 30)	3.1	10, 12, 13, 19, 26	5s, 11s, 15s, 16, 20s
7. (due Tuesday, Oct. 14)	3.2	7, 13, 15, 25	1, 2s, 3, 4s, 9, 21 (see 3D in sec. 3.3), 23 (this is a bit easier than 25), 24s
3.3	2, 12	6, 18s, 21s, 24s
3.4	I think the method described in class [solving directly from the (reduced) row echelon form and then separating the result] is better than the one in the book [setting the free variables to zeros or ones and then combining the results].
3, 11, 17, 20, 34	2s, 6s, 10, 12s, 22, 25s, 31, 33
Please staple the pages together and write your name clearly.

Last modified: October 13, 2008

HOMEWORKS (M = use Matlab)
HW #	Section	HAND IN	Solve only, do not hand in
1. (due Aug. 28)	1.1	6	1, 4, 5, 13* (a,b), 14*
1. (due Aug. 28)	1.2	6 (a,b), 16	2, 3, 5, 8
2. (due Sep. 4)	2.1	10, 11, 16, 18, 27	1, 2s, 3s, 17s, 19s
2. (due Sep. 4)	2.2	6, 11, 12, 19, 21	22
3. (due Sep. 9)	2.3	16, 17, 19, 20, 21, 23, 24	1s, 3s and 4, 12s, 18s, 25s, 27s
4. (due Sep. 18) no penalty if handed in on Tu, Sep. 23	2.4	rules for matrix operations
	2.4	1, 6, 8, 14, 21	5, 9, 11, 13, 30, 36
	2.5	3, 6, 13, 17, 25, 32	1, 4, 7, 12, 14, 26, 29, 33
	2.5	Proof of [A B = I => B A = I for square matrices].
Done on Tuesday, Sep. 16: how to solve A x = b if the A=LU factorization is known (see page 86 in the textbook) apply this for the A=LU factorization computed last time and b=[1 2 3], b=[5 6 7] another example: factor A=[1 1 1; 2 4 5; 3 9 6], solve A x = [1 2 3] uniqueness of A=LU, A=L D U factorizations for A invertible (see problem 18s): If either L or U has 1's on its diagonal, then the A=LU factorization is unique. If both L and U have 1's on the diagonal, then the A=L D U factorization is unique. began section 2.7: pages 96-97, without proofs Done on Thursday, Sep. 18: finished section 2.7 first exam after done with HW's from chapter 2; see review problems above
5. (due Thursday, Sep. 25)	2.6	5, 7, 11, 16	8, 18s, 32, 33, 34, 35 (Matlab later)
5. (due Thursday, Sep. 25)	2.7	3, 11, 16	2s, 20s, 36, proof at bottom of page 109, 22s, 24s
6. (due Tuesday, Sep. 30)	3.1	10, 12, 13, 19, 26	5s, 11s, 15s, 16, 20s
7. (due Tuesday, Oct. 14)	3.2	7, 13, 15, 25	1, 2s, 3, 4s, 9, 21 (see 3D in sec. 3.3), 23 (this is a bit easier than 25), 24s
	3.3	2, 12	6, 18s, 21s, 24s
	3.4	I think the method described in class [solving directly from the (reduced) row echelon form and then separating the result] is better than the one in the book [setting the free variables to zeros or ones and then combining the results].
	3.4	3, 11, 17, 20, 34	2s, 6s, 10, 12s, 22, 25s, 31, 33
	Please staple the pages together and write your name clearly.