Math 321. Linear Algebra. Spring 2011.


Sections:

Books:

Section 001. TR 14:00-15:15. Room: SMLC 356. Syllabus for Math 321 (18697).
Syllabus version from May 8th, 2011.

Main book: Jim Hefferon, Linear Algebra,
Free book available in electronic form at the Author's website
(all information about licenses is given there).
Here is the direct link to the version of the book which is used as a source of homeworks problems.
Here are answers to some homeworks problems.
Alternative/additional reading: Introduction to Linear Algebra book, available at Kenneth Kuttler web-site,
Here is a direct link to the text of the book.

Office hours:


TR 12:00-13:15. Room: SMLC 220.

How grades are assigned?

All homeworks: 100 points (only few randomly chosen problems from the homework will be graded, approximately 8 points for homework).
Two midterm exams: 100 points each (100+100 points).
In class quizes: 50 points.
Final exam: 200 points.
Total: 550 points.
Lowest bondaries for grades (not higher than):
A = 495, B = 440, C = 380, D = 330.
No late HWs are accepted after graded HW is returned. Even before for a late submission you shall get -1 point from the grade.
HW # Homework problems Due date
- Cumulative Final Exam on Tuesday, May 10th. (Solution published)
Training set of problems (don't forget about other problems in the corresponding quizzes(!), HWs and examples in the text):
0) One.III.1, p. 51: 1.7 (a,d), 1.8 (a,b,c), 1.9 (a,b,d);
1) Two.III.1, p. 114: 1.23 (a), 1.24 (a);
2) Three.I.1, p. 164: 1.13 (a,c); Three.II.1, p. 179: 1.17 (a,b,c), 1.18 (a,b), 1.19 (a);
3) Three.II.2, p. 190: 2.22 (a,d), 2.23 (a,b); 4) Three.IV.4, p. 234: 4.14, 4.15, 4.16 (d,f), 4.17;
5) Three.V.1, p. 239: 1.7 (a,d), 1.9 (b,c); Three.V.2, p. 245: 2.12 (a,b), 2.24 (a);
6) Four.I.2, p. 299: 2.7, 2.9;
7) Four.III.1, p. 327: 1.13, 1.14, 1.16(a,b), 1.17(a,b), 1.21;
8) Five.II.2, p. 356: 2.6, 2.7 (a), 2.14, 2.15;
9) Five.II.3, p. 362: 3.20 (a,d,e), 3.21 (a,b), 3.24 (a,b);
10) Three.VI.2, p. 256: 2.9, 2.10, 2.11.
13 Quiz09 on Tuesday, May 3rd. (Solution published) Topic: Gram-Schmidt ortogonalization process.
Quiz10 on Thursday, May 5th. (Solution published) Topic: Least Squares method (Study this!).
Three.VI.1, p. 251: 1.7, 1.8, 1.15, 1.18, 1.19;
Three.VI.2, p. 256: 2.9, 2.10, 2.11, 2.14;
Three.VI.3, p. 264: 3.10 (a,c), 3.11(a,d,f), 3.19, 3.23.
Additional reading (just for fun). MATLAB for Linear Algebra.
May 3rd, 2011, class time.
12 Quiz08 on Thursday, April 28st. (Solution published) Topic: Eigenvalues and eigenvectors.
Four.I.4, p. 315: 4.10, 4.11(a,b), 4.12(a,b);
Four.III.1, p. 327: 1.13, 1.14, 1.16(a,b), 1.17(a,b), 1.19, 1.20, 1.21, 1.27;
Addition to the homework. Complex numbers.
Five.II.1, p. 352: 1.4, 1.7, 1.10;
Five.II.2, p. 356: 2.6, 2.7 (a), 2.8, 2.11, 2.15;
Five.II.3, p. 362: 3.20 (a,d,e), 3.21 (a,b), 3.24 (a,b), 3.25, 3.29, 3.34, 3.40.
April 26th, 2011, class time.
10-11 Quiz08 on Thursday, April 21st, is canceled
Four.I.3, p. 308: 3.14(a,b), 3.15(a), 3.16, 3.22, 3.25, 3.28, 3.30, 3.34;
Four.II.1, p. 321: 1.8(a,c), 1.9, 1.12(a,c), 1.19, 1.26.
April 19th, 2011, class time.
- Quiz07 on Thursday, April 14th. (Solution published) Topic: determinants.
Exam 2 on Tuesday, April 12th. (Solution published) Topics: all covered material since Exam 1, before Four.I.3.
As usual, no calculators or books allowed. You can prepare a page of reference of any formulae etc. you like.
Training set of problems for Exam 2:
Three.II.2, p. 190: 2.23 (a,b);
Three.III.1, p. 200: 1.17 (a,c);
Three.III.2, p. 207: 2.9 (c), 2.13;
Also review Quiz 05;
Three.IV.4, p. 234: 4.16 (d,f);
Three.V.1, p. 239: 1.7 (a,d), 1.9 (b,c);
Three.V.2, p. 245: 2.12 (a,b), 2.24 (a);Have a look at the solution of the quiz 06!
Four.I.2, p. 299: 2.7, 2.9;
Also review the null-space and how to find a basis in the null space for a transformation given by the matrix. Here is an example, study it thoroughly!
None.
9 Quiz06 on Thursday, April 7th. (Solution published) Topic: you will need to be able to change matrix map representation for different bases.
Three.V.1, p. 239: 1.6, 1.7 (a,d), 1.9 (b,c), 1.16, 1.18 (a);
Three.V.2, p. 245: 2.10 (a), 2.12 (a,b), 2.13, 2.15, 2.24 (a);
Four.I.1, p. 295: 1.1, 1.3, 1.4 (a), 1.5 (b), 1.8, 1.9, 1.14, 1.16;
Four.I.2, p. 299 (read examples in this section): 2.7, 2.9, 2.11, 2.18, 2.19.
April 5th, 2011, class time.
7-8 Quiz05 on Thursday, March 31st. (Solution published) Topic: you will need to prove that some map is homomorphism by applying the definition and find a matrix representation of the map.
Three.II.2, p. 190: 2.22 (a,d), 2.23 (a,b), 2.27, 2.34 (a);
Three.III.1, p. 200: 1.11 (a,b,c), 1.12 (b), 1.13, 1.15, 1.17 (a,c), 1.19, 1.21, 1.25 (a,b);
Three.III.2, p. 207: (read corollary 2.5) 2.9 (c), 2.10 (b), 2.13, 2.15, 2.18;
Three.IV.1, p. 212: 1.8 (a,e), 1.14, 1.15, 1.16;
Three.IV.2, p. 218: 2.14 (b,c), 2.16, 2.18, 2.24, 2.30, 2.31;
Three.IV.3, p. 227: 3.23 (a,e), 3.25, 3.27, 3.37, 3.38, 3.39;
Three.IV.4, p. 234: 4.14, 4.15, 4.16 (d,f), 4.17, 4.18, 4.19, 4.20, 4.22, 4.23, 4.29.
March 29th, 2011, class time.
- Exam 1 on Thursday, March 3rd. (Solution published) Topics: all covered material.
There will be no homework and quiz this week.
As usual, no calculators or books allowed. You can prepare a page of reference of any formulae etc. you like.
Training set of problems for Exam 1:
One.I.3, p. 29: 3.15 (a,c,e), 3.16 (a,b,d), 3.22;
One.II.1, p. 38: 1.3;
One.II.2, p. 43: 2.13, 2.14, 2.20, 2.25;
One.III.1, p. 51: 1.9 (a,b,d);
One.III.2, p. 120: 2.17;
Two.I.1, p. 86: 1.20 (a,d), 1.21;
Two.I.2, p. 95: 2.28;
Two.II, p. 106: 1.19 (b,d), 1.24;
Two.III.1, p. 114: 1.19, 1.24 (a), 1.26;
Two.III.2, p. 120: 2.16, 2.17, 2.19 (a,d);
Two.III.3, p. 127: 3.19, 3.23;
Three.I.1, p. 164: 1.13 (a,c), 1.31 (a,b,c);
Three.I.2, p. 172: 2.8 (b,c), 2.17 (a,b).
None.
6 Quiz04 on Thursday, February 24th. (Solution published) Topic: Vector Spaces and Linear Systems.
Three.I.1, p. 164: 1.10, 1.13 (a,c), 1.17, 1.19, 1.26 (a,b,c), 1.31 (a,b,c);
Three.I.2, p. 172: 2.8 (b,c), 2.11, 2.17 (a,b);
Three.II.1, p. 179: 1.17 (a,b,c), 1.18 (a,b), 1.19 (a), 1.22, 1.25 (a,b,c), 1.28, 1.31 (a,b).
March 1st, 2011, class time.
5 Quiz03 on Tuesday, February 22nd. (Solution published) Topic: Linear dependence and independence.
Two.III.1, p. 114: 1.16 (a,d), 1.17 (a,b), 1.19 (see p. 111, Example 1.10), 1.20, 1.21 (a,c), 1.23 (a), 1.24 (a), 1.26, 1.27(a), 1.34;
Two.III.2, p. 120: 2.15, 2.16, 2.17, 2.19 (a,d), 2.20, 2.22, 2.23, 2.26, 2.30(a,b);
Two.III.3, p. 127: 3.16 (a,c,e), 3.17 (b), 3.18 (b), 3.19, 3.20 (a,c), 3.21 (a,c,d), 3.23, 3.26, 3.38 (a).
February 22nd, 2011, class time.
4 Quiz02 on Tuesday, February 15th. (Solution published). Topic: Gauss-Jordan reduction.
One.III.1, p. 51: 1.7 (a,d), 1.8 (a,b,c), 1.9 (a,b,d), 1.12;
One.III.2, p. 59: 2.10 (a,b,c,e), 2.17, 2.20, 2.23;
Two.I.1, p. 86: 1.18, 1.19, 1.20 (a,d), 1.21, 1.25, 1.26, 1.27 (b,c,e), 1.29, 1.37;
Two.I.2 (read examples in this section), p. 95: 2.20, 2.21, 2.22, 2.23, 2.24 (a,c,e), 2.26 (a,b,f), 2.27, 2.28, 2.33;
Two.II, p. 106: 1.18 (a,c), 1.19 (b,d), 1.20 (a,b), 1.21(a,f), 1.24, 1.26, 1.32, 1.39.
February 15th, 2011, class time.
2-3 Quiz02 on Thursday, February 3rd is canceled.
One.I.3, p. 29: 3.15 (a,c,e), 3.16 (a,b,d), 3.18 (a), 3.19, 3.20 (a,c,e), 3.21 (a,d), 3.22;
One.II.1, p. 38: 1.2, 1.3;
One.II.2, p. 43: 2.10 (a,c,e), 2.11, 2.12, 2.13, 2.14, 2.15, 2.20, 2.25, 2.38.
February 8th, 2011, class time.
1 Quiz01 on Thursday, January 27th. (Solution published) Topic: Gauss' method for systems of linear equations.
One.I.1, p. 9: 1.17 (a,b), 1.18 (a-f), 1.19, 1.20, 1.22, 1.25, 1.28;
One.I.2, p. 18: 2.15, 2.16, 2.18 (a,d,e), 2.19 (a,c), 2.20 (a,b), 2.23, 2.26, 2.27(a), 2.30(a).
January 27th, 2011, class time.