MAT 211.01 Homework Assignments

Spring 2006

# Problems Due Date
Homework 1
 Mostly the HW will be from Bretscher, but I wrote it out this week since you may not all have the book yet. Download it by clicking on the blue prompt to the left. 1/25/06

Solutions to Homework 1
Homework 2
 sec 1.1: 20; sec 1.2: 6, 10, 18, 22, 26, 34, 36, 46. Also: (a) Find parametric equations for the line of intersection of the planes 2x+3y+4z=1 and x+y+z=1. (b) Find the equation of the plane through the point (1,1,1) and perpendicular to the line (x,y,z) = (1+2t,2-3t,t). 2/1/06

Solutions to Homework 2
Homework 3
 sec 1.3: 6, 14, 20, 30, 36, 49. T/F questions on p 38: 20; sec 2.1 6, 10, 14. (This should be easier homework.) 2/8/06

Solutions to Homework 3
Homework 4
 sec 2.1: 42; sec 2.2: 4 (draw a diagram), 26(a)-(d),30,44 (draw a diagram); sec 2.3: 20,30; sec 2.4: 4,14,28. 2/15/06

Solutions to HW 4 Page 1 Page 2 Page 3
Homework 5
 sec 2.4: 40, 50, 52, 86; sec 3.1: 22, 24, 44; sec 3.2: 2, 16, 32. 2/22/06

Solutions to HW 5 Page 1 Page 2 Page 3
Half Homework 6
 Sec 3.2: 22, 46; Sec 3.3: 16, 26, 30. 2/27/06

Solutions to HW 6 Page 1
Homework 7
 Sec 3.4: 8, 10, 14 (read sec 3.4 through Def 3.4.1); Ch 3 T/F questions: 4, 14, 16; Sec 4.1: 4, 6, 20, 30. Solutions to HW 7 3/8/06

Solutions to Midterm I Page 1 Page 2 Page 3 Page 4
Homework 8
 Sec 4.1: 36, 38; Sec 4.2: 6, 16, 20, 30, 56; Sec 4.3: 4, 6, 20. Solutions 3/15/06
Homework 9
Sec 4.3: 23, 24, 46, 60; Sec 5.1: 2, 6, 26. Sec 5.2: 6, 32. Solutions 3/22/06
Half Homework 10
 Sec 5.3: 4, 8, 10, 22, 36 Solutions 3/27/06
Half Homework 11
 Sec 5.5: 10; Sec 6.1: 8, 30, 34. Solutions 4/5/06
Homework 12
 Sec 6.2: 2, 10, 12, 14, 30, 38; Sec 6.3: 2, 7, 24, 30. Solutions 4/19/06
Homework 13
 Sec 7.1: 10, 16, 18, 22, 34, 50; Sec 7.2: 10, 22(for n=2,3 only), 24, 26. Solutions 4/26/06
Half Homework 14
 Sec 7.3: 6, 20, 36; Sec 7.4: 8, 16 Solutions 5/1/06

Your answers will be graded both on the correctness of the mathematics and on the way in which you have written it down. Always explain what you are doing.

IMPORTANT: Answers to "True or False" and "Show that..." problems MUST include a full justification.

For example... If you are given the statement "all odd integers are prime," first determine whether it is true or false. Then make the resulting claim, and give its justification. The following is acceptable:

CLAIM: Not all odd integers are prime. PROOF: Even though 9 is odd, it is not prime, since 9 = (3)(3).
(This is not the only possible answer -- you could use, say, 15 or 25 instead of 9. The point is that this is the level of precision expected in your answer.)

If you are given the statement "the product of two odd integers is odd," first determine whether it is true or false. Then make the resulting claim, and give its justification. The following is acceptable:

CLAIM: The product of any two odd integers is odd. PROOF: If m and n are odd integers, then m=2k+1 and n=2l+1 for some integers k and l, so mn = (2k+1)(2l+1) = 4kl+2k+2l+1 = 2(2kl+k+l)+1. Therefore mn is odd.

However, the following is NOT acceptable:
CLAIM: The product of any two odd integers is odd. PROOF: 5 and 7 are odd. (5)(7)=35, and 35 is odd.
(Since the claim concerns ANY pair of odd integers, not just 5 and 7, checking the statement for just one pair of odd integers does not constitute a valid answer.)

The only difference between a "True or False" problem and a "Show that..." problem is that with the latter, you are given a statement which is KNOWN to be true and then asked to justify it.