MTH 42, Spring 2014

Text: Linear Algebra and Its Applications, 4th Edition. David C. Lay, Addison Wesley 2012

I will be following the fourth edition but the third edition of the text also works. Here is a list of topics that we'll cover. Sections and page numbers refer to the fourth edition but shouldn't be very different in the third.

Section	Topic	Page
1.1	Systems of linear equations	2
1.2	Row reduction and echelon forms	12
1.3	Vector equations	24
1.4	The matrix equation \(A \mathbf{x}= \mathbf{b}\)	34
1.5	Solution sets of linear systems	43
1.7	Linear independence	55
1.8	Introduction to linear transformations	62
1.9	The matrix of a linear transformation	70
2.1	Matrix operations	92
2.2	The Inverse of a Matrix	102
2.3	Characterizations of invertible matrices	111
3.1	Introduction to determinants	164
3.2	Properties of determinants	169
3.3	Cramer's rule, volume and linear transformations	177
4.1	Vector spaces and subspaces	190
4.2	Null spaces, column spaces, and linear transformations	198
4.3	Linearly independent sets; bases	208
4.4	Coordinate systems	216
4.5	The dimension of a vector space	225
4.6	Rank	230
4.7	Change of Basis	239
5.1	Eigenvectors and eigenvalues	266
5.2	The characteristic equation	273
5.3	Diagonalization	281
5.4	Eigenvectors and linear transformations	288
5.5	Complex Eigenvalues	295
6.1	Inner product, length, and orthogonality	330
6.2	Orthogonal sets	338
6.3	Orthogonal projections	347
6.4	The Gram-Schmidt process	354

You are expected to read the textbook both before and after each class meeting. Some of the homework depends on carefull reading of the textbook and at the beginning of each class meeting I will assume that you have at least glanced the setion that is to be covered ahead of time.

Homework: Homework from the text will be assigned at the end of each class. It is essential that you do the homework. In each homework set there will be some designated problems, appearing in bold font in the table bellow, that you have to turn in. Ocassionally there may be some additional handouts with homework that you have to turn in.

Section	Homework	Page
1.1	1-17 (odd), 19, 21, 23, 24, 27	10
1.2	1-17 (odd), 19, 21, 22, 29	21
1.3	1-15 (odd), 21, 23, 24, Handout	32
1.4	1-15 (odd), 23, 24, 31	40
1.5	1-17 (odd), 23, 24, 31, 33	47
1.7	1-19 (odd), 21, 22, 27, 31	60
1.8	1-19 (odd), 21, 22, 23	68
1.9	1-19 (odd), 21, 23, 24, 35	78
2.1	1-13 (odd), 15, 16, 23, 25	100
2.2	1-7 (odd), 9, 10, 11, 12, 13	108
2.3	1-7 (odd), 11, 12, 13, 15, 33	115
3.1	1-17 (odd), 39, 40, 41, 42	167
3.2	1-13 (odd), 23, 25, 27, 28, 31, 33	175
3.3	1-9 (odd), 13, 17, 19, 25, 29, 31	184
4.1	1-17 (odd), 21, 23, 24, 27, 29	195
4.2	1-19 (odd), 25, 26, 31, 33, 34	205
4.3	1-15 (odd), 21, 22, 23, 29, 33	213
4.4	1-13 (odd), 15, 16, 17, 19, 25	222
4.5	1-17 (odd), 19, 20, 21, 23, 29, 31	229
4.6	1-15 (odd), 17, 18, 23, 25	236
4.7	1-9 (odd), 11, 12, 13	242
5.1	1-19 (odd), 21, 22, 23, 25, 26, 31	271
5.2	1-17 (odd), 19, 21, 22, 23, 24	279
5.3	1-19 (odd), 21, 22, 23, 25, 27, 29	286
5.4	1-15 (odd), 17, 19, 20, 21, 27	293
5.5	1-19 (odd), 21, 23, 24	300
6.1	1-17 (odd), 19, 20, 24, 31	336
6.2	1-21 (odd), 23, 24,*25*, 28	344
6.3	1-15 (odd), 19, 21, 22, 23	352
6.4	1-11 (odd), 17, 18	359

Exams: There will be a midterm and a final. The final exam will cover all the material.

Grading: Your grade will be calculated as follows:

Homework	20%
Midterm	30%
Final	50%

There also will be some projects assigned for extra credit.

• Proof of the Parallelogram rule

• Additional Review problems for the final

• Midterm exam
• Spring Break Take Home Exam

There is an electronic mailing list for this class hosted by Google Groups. It is required that students join the list. To subscribe please enter your emaail address in the form bellow, and click on the `Subscribe' button.

After that you should receive a notification email requesting you to verify that you really want to subscribe to the group. Please follow the directions in that email. If you have trouble subscribing to the group please let me know.