Math 313.002 Linear Algebra Morrow, Fall 2009
Meetings:
TR 3:05 pm – 4:20
pm, SENG B134
Instructor: Greg
Morrow
Office:
EN 272, (719) 255
–3184, gmorrow@uccs.edu
Hours: TR: 1:45 – 2:55, or by appointment
Prerequisite:
Calculus I (Math 135)
Text: Introduction to Linear Algebra, 4th ed., by Gilbert
Strang (2009),
MIT Open Course
Ware website based on the 3rd edition of this text: http://ocw.mit.edu/OcwWeb/Mathematics/18-06Spring-2005/CourseHome/
Description:
Linear algebra is a fundamental computational tool for solving applied
mathematics problems involving several variables. At first the
hand-computational side will be stressed to lay a ground-work for the
concepts. After this, more emphasis will
be placed on the conceptual framework; for example the four fundamental
subspaces theme will recur in problems of later chapters. For reading of the
first 2 chapters of the text, some review of vectors and equations of lines and
planes in 2 and 3 dimensional space may be useful (say from the first chapter
of a calculus 3 book). This material and ongoing supplementary material
throughout the course will also be covered by notes in pdf (see Notes 1, Notes
2, etc. below). The Matlab computer algebra software will be introduced
somewhat later in the course as a way to illustrate the concepts being covered
but this software is not required for students to have—those who wish to become
more familiar with it may find it available on EAS servers with instructions
for connecting to it via remote desktop client, say, at: http://www.eas.uccs.edu/it/using_rdp.shtml.
The course covers chapters 1- 6 of the text. A key focus will be on problems
appearing in the text.
Homework and Tests:
Homework will be assigned and collected weekly. There will be two mid-semester tests, as well
as a final exam. The final exam will
test primarily the material covered after the second midterm exam. Calculators will not be allowed on tests.
Homework will count 20% of the course grade, each mid-semester test will count
26%, and the final exam will count 28%. There will be no make-up for late
homework; one homework assignment may be dropped. Arrangements for make-up
exams must be made in advance except in extraordinary circumstances. Also the
student is responsible in the event that a make-up exam is approved to make an
appointment to take the exam with disability services (X 3354 ) and then report
this appointment to Morrow via email.
Final exam:
Thursday, December 17, 1:40 pm – 4:10 pm.
Grading.
90’s => grade of A, 80’s => B or better, 70’s => C or
better. Half grades (e.g. B+) are possible.
Math
313.002 Linear Algebra Morrow, Fall 2009
Syllabus
and Homework (revised
Dec. 7, 2009)
Aug 25. 1.1-1.2: Vectors, linear combinations, angle
between vectors
Aug 27. 2.1-2.2: Elimination of variables
HW 1
1.1: #2, 8, 16; 1.2: #7a,b, 12, 13, 27;
2.1: #5, 7, 21,
29; 2.2: #2, 12, 21, 26.
Due: Tues, Sep 1.
Sept 1. 2.3-2.4:
Elimination and permutation matrices, and block multiplication
Sept 3. 2.5: Inverse Matrices
HW 2
2.3: #3, 17, 23,
26; 2.4: #6, 9, 10,
26, 29.
Due: Thurs, Sept
10.
Sept 10. 2.6-2.7: LU Factorization;
Symmetric Matrices and the Transpose
HW 3
2.5: #4, 10b, 23, 30, 34; 2.6: #8, 9a, 15, 20;
2.7: #1, 2, 5, 15
(Extra Credit).
Make 2.5 #34 extra credit. Simply verify the answers in back of the text assuming 2by2 sub-matrices and using block multiplication!
Due:
Thurs, Sept 17. (NOTE CHANGE of due date)
Sept 15.
3.1: Vector Spaces and
Subspaces
Sept 17.
3.2: Nullspace
HW 4
3.1: #3, 10, 20a,
23, 24;
3.2: #1, 2, 5,
17, 18, 23.
Due: Thurs, Sept 24.
Sept 22. Review
EXAM 1, Tues, Sept. 29. Covers
1.1-3.2 (excluding 1.3).
Sept 24. 3.3: Rank and row reduced form
Oct. 1. 3.4: Complete solution of a linear system
HW 5
3.3: #2b, 7
(omit), 10, 19;
3.4: #1, 3, 5,
8b, 19, 31(extra cr.).
Due: Tues, Oct. 6.
Oct. 6. 3.5:
Oct
.8: 3.6: Four subspaces
HW 6
3.5: # 1, 2, 7,
8, 13, 16;
3.6: # 3, 18, 23,
24.
Due: Thurs, Oct 15.
Oct. 13. 4.1: Orthogonal Complement
Oct. 15. 4.2: Projections
HW 7
4.1: # 6, 11, 21,
28
4.2: # 1, 5, 6,
11, 12 13, 17.
Due: Thurs, Oct 22.
Oct 20. 4.3: Least squares approximation
Oct 22. 4.4: Gram-Schmidt and QR factorization
HW 8
4.3: # 1, 9, 20,
21;
4.4: # 10, 13,
14, 21, 23.
Due: Tues., Nov. 3 (DUE DATE POSTPONED as of
Oct. 29)
Sample
Solution Review for Exam 2 (typo:
#2(b): particular solution x2=t-s, x1=2s-t, x3=0.)
Oct 27. Review
EXAM 2, Tues, Nov. 3. Covers
3.3-4.4
Oct. 29. 5.1: Determinants
Nov 5. 5.2-5.3: Permutation and co-factor expansions: volume.
HW 9
5.1:
# 1, 14, 15, 21, 22;
5.2: # 4, 17, 19;
5.3: # 1, 4, 8,
16, 24.
Due: Thurs, Nov 12.
Nov 10.
6.1: Introduction to
Eigenvalues
Nov
12. 6.2: Diagonalizing a Matrix
HW 10
6.1:
# 1, 12, 24, 26, 32;
6.2: # 1, 2, 16, 17,
33 (extra cr.).
Due: Thurs, Nov 19.
Nov 17.
6.4: Symmetric matrices
are (orthogonally) diagonalizable
Nov
19. 6.5: Positive Definite Matrices
HW 11
6.4: # 4, 5, 12,
18, 25, 26;
6.5: # 1, 2, 5,
9, 17, 22, 24.
Due: Thurs, Dec. 3.
Dec 1.
6.6: Similar matrices
Dec
3. 6.7: Singular value decomposition
HW 12
6.6: # 1, 4, 5,
9, 20-- Sect. 6.6 will be extra credit, total 10 points extra here;
6.7: #
1, 2, 3, 6, 7.
Due: Thurs, Dec 10.
(Matrix in prob. #7 is corrected from the original; row by row, A=[0 1;1 1; 1 0].)
Typos: #5. First column of Q is 2/3, 2/3, -1/3 (omit square root signs). #6. Matrix A should have zeros in the 1,3 and 3,1 positions and entries -1/2 instead in the 2,3 and 3,2 positions. The other entries are correct. In the reduction of A, the diagonal entries of U are still 1, 3/4, and 2/3 in that order. The three upper left (minor) determinants of A are still 1, 3/4, and 1/2, in that order. The fact that det(A)=1/2 follows by taking the product of the diagonal entries of U.
Dec 8. Review
Dec 10. Review
FINAL EXAM, Thurs, Dec 17, 1:40- 4:10 pm. Covers 5.1-6.7 (excluding 6.3,6.6)