MA242 A1 - Linear Algebra

MA242 A1 - Linear Algebra - Fall 2009

Lecture: T,Th 3:30-5pm in PSY B55
Discussion: M 1-2pm in PSY B49

Welcome to the Linear Algebra (MA242, section A1, Fall 2009) course webpage! If you need any information that you can't find here, please email me.

Linear algebra is the subject that made me want to become a mathematician. When I was an undergraduate, my linear algebra professor made me attend a research seminar on this paper, which you should be able to understand by the end of this course. In it, the authors use linear algebra to study the population dynamics of an endangered species of sea turtle. Among other things, their results indicated that it was important to protect the turtles from the adverse effects of certain types of fishing. In fact, they even used their research to help get legislation passed to do exactly that. For more information, click here.

Contact Information

Instructor: Margaret Beck
Office: MCS 233
Phone: 617-358-3314
Email: mabeck -at- math.bu.edu
Office Hours: T 11-12 and Th 10-11, or by appointment. (See the announcements for office hours during the reading period.)

Announcements

Final exam will cover: all the material discussed in class and covered on the homework throughout the semester. This includes Chapters 1.1-1.5, 1.7-1.9, 2.1-2.3, 3.1-3.3, 4.1-4.6, 5.1-5.6, 6.1-6.4, 6.7 from the book and anything additional that was discussed in class (such as the applications we discuss during the last couple lectures).

Extra office hours during study period: My office hours during the study period will be Monday, Dec 14, 3-5pm, and Tuesday, Dec 15, 3-5pm.

Important Dates:

Final Exam: Wednesday, Dec 16, 3-5pm, in PSY B55

Course Info

Syllabus and detailed course info:[.pdf] [html]
Textbook: "Linear Algebra and its Applications," 3rd Ed., by David C. Lay; Addison Wesley, 2003. ISBN number 0-201-77014-8.
Note: If you have a slightly different edition of this textbook, it is likely it will work fine. Please check with me to be sure.
Grading policy: 40% final exam, 25% each test, 10% homework average.

Non-graded Homework Assignments

Assigned Thursday, Sept 3: Section 1.1: 1, 7-25 odd
Assigned Tuesday, Sept 8: Section 1.2: 1, 7-13 odd, 17-31 odd
Assigned Thursday, Sept 10: Section 1.3: 1-5 odd, 9-13 odd, 17-25 odd; Section 1.4: 1, 3, 11-25 odd, 29-35 odd
Assigned Tuesday, Sept 15: Section 1.5: 7, 11-17 odd, 23-31 odd, 39; Section 1.7: 1-11 odd, 15-19 odd, 21, 23, 27, 31, 37, 39
Assigned Thursday, Sept 17: Section 1.8: 1-11 odd, 17-25 odd, 29, 35
Assigned Tuesday, Sept 22: Section 1.9: 1,3,7,9,15,21-27 odd, 31, 35
Assigned Thursday, Sept 24: Section 2.1: 1,3,7-11 odd, 15, 21-27 odd; Section 2.2: 1,5,9,13,19,21,23,25,31
Assigned Tuesday, Sept 29: Section 2.3: 1-7 odd, 11, 15, 17, 21, 23, 27, 35; Section 3.1: 1, 9-13 odd, 19-29 odd, 37
Assigned Thursday, Oct 1: Section 3.2: 9,11,15-25 odd, 29, 31, 37, 39; Section 3.3: 1,3,11,13,17,21,23,27,29
Assigned Thursday, Oct 15: Section 4.1: 1-15 odd, 21-25 odd, 29-33 odd
Assigned Tuesday, Oct 20: Section 4.2: 1,5,7,13-17 odd, 21-35 odd
Assigned Thursday, Oct 22: Section 4.3: 3-15 odd, 19-25 odd, 29-33 odd; Section 4.4: 3, 7-15 odd, 19-25 odd, 29, 31
Assigned Tuesday, Oct 27: None
Assigned Thursday, Oct 29: Section 4.5: 5-25 odd, 29, 31; Section 4.6: 1-17 odd, 21, 23, 27, 29
Assigned Tuesday, Nov 3: Section 5.1: 5,7,13,17-25 odd, 31
Assigned Thursday, Nov 5: Section 5.2: 7,9,11,15,17,19,21
Assigned Tuesday, Nov 10: Section 5.3: 1,3,5,9,11,19-31 odd
Assigned Tuesday, Nov 17: Section 5.4: 1-13 odd, 23, 29
Assigned Thursday, Nov 19: Section 5.5: 1-9 odd 13, 15, 21
Assigned Tuesday, Nov 24: Section 6.1: 1-19 odd, 23-31 odd
Assigned Tuesday, Dec 1: Section 6.2: 3-27 odd, 33
Assigned Thursday, Dec 3: Section 6.3: 1,3,9-23 odd; Section 6.4 1-11 odd.
Assigned Tuesday, Dec 8: Section 6.7: 1-17 odd, 21-25 odd
Assigned Thursday, Dec 10: Section 5.6: 1,3,5

Graded Homework Assignments (each assignment worth 10 points unless otherwise noted)

HW 1, Due Tuesday, Sept 15, by 3:30pm: 1.1 #24, 1.2 #20, 1.3 #12
Solutions: #24 True, False, False, True; #20 a) h=9, k anything but 6, b) h anything but 9, c) h=9, k=6; #12 b is not a linear combination of the given vectors
HW 2, Due Tuesday, Sept 22, by 3:30pm: 1.4 #18, 1.5 #16, 1.7 #38
Solutions: #18 Row reduction shows only three rows of B have a pivot, and so the answer is NO; #16 X = [-5 3 0] + x3 * [-4 3 1], which is a line through [-5 3 0] and parallel to the solution set of the homogeneous problem; #38 True. You can prove this using a proof by contradiction. For a complete proof see me.
HW 3, Due Tuesday, Sept 29, by 3:30pm: 1.8 #20, 1.9 # 26, 2.1 #22
Solutions: #20 A = [-2, 7; 5, -3], #26 It is not 1-1 but it is onto; #22 For a proof, see me.
HW 4, Due Thursday, Oct 15, by 3:30pm: 2.2 # 32, 2.3 # 36, 3.1 #10
Solutions: #32 By doing row reductions on the matrix augmented with the identity matrix, we find the inverse does not exist, #36 See me for a complete proof, #10 -6
HW 5, Due Tuesday, Oct 20, by 3:30pm: 3.2 #42, 3.3 #12, 4.1 #12
Solutions: #42 See me for a complete proof, 3.3 #12 adjA = [-1 3 7 // 0 0 5 // 2 -1 -4] and A^(-1) = (1/5)adjA, 4.1 #12 W = span{ [1 1 2 0], [3 -1 -1 4]}, so it is a subspace.
HW 6, Due Tuesday, Oct 27, by 3:30pm: 4.2 #24, 4.3 #26, 4.4 #14
Solutions: #24 w is in both ColA and NulA; #26 Since 2sin(t)cos(t) = sin(2t), the basis is sin(t) and sin(2t); #14 [7 -3 -2].
HW 7, Due Tuesday, Nov 3, by 3:30pm: 4.2 #28, 4.3 #16, 4.4 #30
Solutions: #28: Since [ 0 1 9] is in ColA, so is 5[0 1 9], since ColA is a subspace and therefore closed under scalar multiplication. Thus, the second system must also have a solution. #16 {v_1, v_2, v_3}, #30: The vectors are linearly dependent.
HW8, Due Tuesday, Nov 10, by 3:30pm: 4.5 #6, 4.6 #4, 4.6 #20
Solutions: #6: Basis = {[3 6 -9 -3], [6, -2, 5, 1]} and the dimension is 2. #4: The rank A = dim Nul A = 3; the basis for Col A is the pivot columns of A, the basis for Row A is the nonzero rows of B, and after putting B into RREF, we see the basis for Nul A is {[2 1 1 0 0 0], [-9 -7 0 1 1 0], [ -2 -3 0 2 0 1]}; #20: No, because the rank of the corresponding matrix is 6, and hence there is a solution for each right hand side.
HW9, Due Tuesday, Nov 24, by 3:30pm (worth 15 points): 5.1 #26, 5.2 #12, 5.3 #18, 5.4 #6, 5.5 #4.
Solutions: See me for complete solutions.
HW10, Due Tuesday, Dec 8, by 3:30pm (worth 15 points): 6.1 #26, 6.2 #10, 6.3 #16, 6.3 #24, 6.4 #12
Solutions: See me for complete solutions.

Test/Exam info

Solutions to our final can be found here.
Solutions to our second test can be found here.
Solutions to our first test can be found here.
On Professor Blanchard's webpage (near the bottom) you can find some examples of old tests and exams he's given, which are similar to those I'll give in this class.