**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

Please read it carefully. Anytime you have questions about the course, you can reach me by email at

or during my office hours:

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:**

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

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.

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.

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).

I've written up solutions to this one.