# Math 321. Linear Algebra. Spring 2011.

## 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
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.

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.
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.