Math 2270-3 Linear Algebra


Instructor: Mladen Bestvina

Office: JWB 210

Web page: http://www.math.utah.edu/~bestvina/2270

Office Hours: after class or by appointment

Textbook: Linear Algebra 3rd Edition, by Serge Lang, Springer Verlag

Time: MWF 16:35-17:50

Room: JWB 308


The course is an honors version of 2270 and it will be taught in a more abstract manner than the regular sections. I plan to cover at least the first 8 chapters of the textbook, and maybe more if the time permits.

The grades will be based on homework and class participation.


There are a few more books you might find useful:
If a concept we discuss is unclear you may want to consult some of these books.

You can contact me by email.



Homework 1, due Sept 2.

We'll discuss how to solve a system of linear equations, which is not in Lang's book. I'll follow Treil's book above, the first 4 sections of chapter 2.


Homework 2, due Sept 11. Lang p.36-42: #18(e), 19, 20, 32, 35, 39.
    Hint for 32: Use that t(AB)=tBtA
    Hint for 35: Show that if A has entries 0 below the kthdiagonal (i.e. j-i<k implies aij=0) and B has entries 0 below lth diagonal then AB has entries 0 below (k+l)th diagonal. By popular demand, here is the solution to #35.

Homework 3, due Sept 16. Treil's book Ch.2: p.46: 2.2, p.51: 3.1, 3.2, 3.3 a,c, p.54: 4.1
    Hint for 3.3c: Rearrange the order of vectors and then it's already in echelon form!

Homework 4, due Sept 23. Lang p.58:#15,18, p.63:#3,5, p.70 #8a,10

Homework 5, due Sept 30. Lang p.93, #1(b), 8(e), 8(f), p.103 #1,2, p.111 #0,1

Homework 6, due Oct 7. Lang p.103, #3, p.111 #2b, p.117 #1g,3,6. Read Treil's book sections 4-5 on p.136-146 and do #4.1,4.4 on p. 141.

Homework 7, due Oct 21.

Homework 8, due Oct 28: Lang p.154 #1a,5b, Treil p.85 #3.4,3.9,3.10, p.89 #4.1, also write the given permutation as a product of transpositions

Homework 9, due Nov 4: Treil p.94 #5.2,5.3,5.4,5.5, Lang p.177, #2.

Homework 10, due Nov 11: Lang p.199: #4,5 (hint: use the char poly), p.213: #8d, 10,11,15 (hint: if ABv=λv apply B but watch out for λ=0)

Homework 11, due Nov 18: Lang p.183: 1,2,6,11,12,15 (warning: this homework is a bit harder than usual)

Homework 12, due Nov 25: Lang p.218 #3, p.223 #9f, 16d, p.226 #1,4, Treil p.170 #2.6,2.8.

The last homework will be assigned on Monday and will be due the following Monday. Happy Thanksgiving!

Homework 13, due Dec 7: Lang p.260 #2, p.261 #2, p.266 #1,2. Hint on #1: Define D to be multiplication by λ on the generalized λ-eigenspace.

    I am not assigning #6,7 on p.267, but if you want to try a little "research project" you could give it a shot.

That's all folks! If you feel like it look at the collection of linear algebra problems by Prof. Jerry Kazdan and see how many you can solve.