Math 54 - Section 5 - Summer 2011

Welcome to Math 54! This is your instructor, Alex Kruckman. There's lots of info about the course in the

Syllabus!

Please read it carefully. Anytime you have questions about the course, you can reach me by email at
(my last name) at math.berkeley.edu

or during my office hours:
1056 Evans on Mondays 2-3,
Wednesdays 2-3, and
Thursdays 11-12.

Homework:

Homework Statistics

Look here for homework assignments.

HW 1 (due Fri. 6/24): 1.1 #4, 22, 26; 1.2 #4, 12, 20; 1.3 #10, 12, 16; 1.4 #2, 4, 16, 22; 1.5 #10, 14, 20, 40; 1.7 #2, 10, 32, 34, 36; 1.8 #2, 10, 12; 1.9 #2, 10, 18.
Challenging Problems (optional): 1.1 #33, 34; 1.2 #29, 30, 31; 1.4 #32, 34; 1.8 #24, 31.
Problems scanned from textbook
Solutions

HW 2 (due Tues. 6/28): 2.1 #2, 4, 7, 8, 11, 22, 27, 28, 33 (Hint: What is the entry in the ith row and jth column of (AB)^T? What about in (B^T)(A^T)?); 2.2 #3, 6, 14, 21, 22, 23, 24, 30, 32.
Optional Problems: 2.1 #23, 24, 25, 26; 2.2 #25, 26.
Problems scanned from textbook
Solutions

HW 3 (due Fri. 7/1): 2.3 #2, 4, 6, 8; 3.1 #10, 12, 14, 37, 38; 3.2 #8, 22, 24, 31, 32, 34
Solutions

HW 4 (due Tues. 7/5): 4.1 #2, 8, 10, 28, 30; 4.2 #2, 6, 20, 22, 24, 27
Optional Problems: 4.1 #31, 32, 33, 34; 4.2 #31, 32, 34
Solutions

HW 5 (due Tues. 7/12): 4.3 #2, 4, 6, 8, 14, 20, 24, 34; 4.4 #2, 4, 6, 8, 14, 18, 30, 32 (for #30 and 32, see Examples 5, 6, 7 in the section)
Optional Problems: 4.3 #31, 32; 4.4 #19, 20, 25, 26
Solutions

HW 6 (due Fri. 7/15): 4.5 #2, 6, 8 (note: this is intended to be a subspace of R^4), 12, 22, 24; 4.6 #2, 4, 6, 8, 10, 12, 20; 5.1 #2, 4, 6, 8, 10, 16, 18, 31, 32; 5.2 #2, 6, 10, 14, 16, 18
Optional Problems: 4.5 #26, 28; 4.6 #27, 28, 29, 30; 5.1 #25, 26, 27
Solutions

HW 7 (due Tues. 7/19): 5.3 #6, 8, 10 , 12, 18, 20, 23, 24, 25, 26; 5.4 #2, 4, 6, 8, 10, 12, 16
Optional Problems: 5.3 #31, 32; 5.4 #20, 27, 29
Notes: 5.3 #12, 18: There is a hint on page 293 (just before the problems). 5.3 #23-26: You will be able to do these after Monday's lecture or after reading pages 291 and 292 in the book (the very end of section 5.3). 5.3 #31-32: "Construct" just means "write down".
Solutions

HW 8 (due Tues. 7/26): 5.5 #2, 4, 6; Ch. 5 Supplementary Exercises (p. 310) #10, 18; 6.1 #2, 4, 6, 8, 10, 14, 16, 18, 24; 6.2 #2, 4, 6, 8, 10, 14, 20, 32, 33.
Solutions

HW 9 (due Fri. 7/29): 6.3 #2, 4, 8, 10, 12, 16; 6.4 #4, 8, 10, 12; 6.5 #2, 4, 6, 8, 10, 12 (in 10 and 12, note that the columns of A are orthogonal), 14, 25.
Optional Problems: 6.3 #23, 24; 6.5 #19, 20, 21, 22.
Solutions

HW 10 (due Tues. 8/2): 4.2 #2, 4, 6, 14, 16, 18, 21, 22, 24, 26; 4.3 #6, 8, 22, 24, 28 (you should use a graphing calculator to obtain the sketches); 6.1 #2, 4, 6, 16, 18 (a fundamental solution set is a basis for the solution space S), 24.
Optional Problems: 4.2 #36, 37; 4.3 #38, 40; 6.1 #26.
Solutions

HW 11 (due Fri. 8/5): 4.4 #10, 18, 34; 4.5 #2, 4, 6, 28; 4.6 #2, 6, 10; 6.2 #2, 6, 14.
Optional Problems: 4.6 #20, 6.2 #25.
Solutions

HW 12 (due Tues. 8/9): 9.1 #4, 8, 12; 9.4 #2, 6, 24; 9.5 #12, 26, 34; 9.6 #2, 14; 9.8 #18, 20
Notes: 9.4 #24: This is easy. Don't overthink it. col(x,y,z) just means the column vector with entries x, y, and z. 9.8 #18, 20: You'll be able to do these after Monday's lecture or after reading the section carefully.
Solutions

Materials:

Look here for worksheets, handouts, and solutions to practice problems.

6/23 - Into and Onto Linear Transformations
6/27 - The 2x2 Determinant
6/29 - Cramer's Rule - Solutions
7/06 - Midterm 1 Concept Review
7/22 - Midterm 2 Concept Review
7/28 - Differential Equations Lecture Notes
8/10 - Final Exam Concept Review
8/11 - Final Review - True, False, or Nonsense? - Solutions - Graded worksheets

Sample Exams (Midterm 1):
Here are some sample midterms. I've indicated which problems are about material we've covered.
Ribet, Fall '05 - All (except the last part of #3 about perpendicular vectors). Also, here are some Solutions.
Lenstra, Fall '94 - Problems 1, 2, 4. I also wrote up some solutions to this one. You're welcome!
Gu, Fall '07 - All (Notes: Problem 3 is harder than anything on my midterm. In Problem 5, the "image of a matrix" means the column space, or the range of A as a linear transformation)
Vojta, Spring '01 - Problems 1(a)-(d), 2, 3, 4, 6, 7.

Midterm 1: Solutions, Statistics

Sample Exams (Midterm 2):
Here are some sample midterms. I've indicated which problems are about material we've covered.
Ribet, Fall '05 - All (except the last part of #3 about the orthogonal basis). Also, here are some Solutions.
Lenstra, Fall '94 - Problems 1, 2, 4.
Bergman, Spring '96 - Problems 1(all), 2(a,b,e,f), 3.
Vojta, Spring '01 - Problems 1 (RS and CS are row space and column space), 2, 5, 6, 7. I also wrote up some solutions to this one.

Midterm 2: Solutions, Statistics

Sample Exams (Final):
Here are some sample finals. I've indicated which problems are similar to problems I might give.
Ribet, Fall '05 Problems 1, 2, 3, 4, 6, 7 (not 5, 8, or 9). Also, here are some Solutions.
Lenstra, Fall '94 Problems 1, 2, 3 (not 4 or 5).
Tener, Summer '09 Problems 1, 2, 3, 6, 7 (not 4 or 5).
Tucker-Simmons, Summer '09 Problems 1, 2, 3, 4, 6 (not 5 or 7 - although note that 7 is an extra credit problem - I could conceivably do something like this). Notes: In the first problem (1.1), there is a typo: the differential equation should be y'' + 10y' + 25y = 0. In problem 2.3, "orthogonally diagonalize" means that the basis of eigenvectors should be an orthogonal basis.
I've written up solutions to this one.

Final: Solutions, Statistics