I'm going to be the TA of a linear algebra course this semester but i have problems for finding good problems to show, i've been looking on mathexchange but they are too "of the book" and i ran out of ideas for problems made by me, does anyone have good source material for this?
>>7963840
first year undergrad in Electrical Engineering here
Linear Algebra is gay, and I have proved it mathematically
That's all I have to say about that.
Although, my course used "Introduction to Linear Algebra" by Johnson, Riess, and Arnold.
It sucks too.
Give them a 5x5 fully occupied matrix and let them calculate all Eigenvalues. This will them a while.
>>7963840
do you want for all or just end game
>>7963866
>>7963879
2) is just cute, I love it,
Make 3 4x4 tho, just put those cofactors to the test
>>7963840
Steal shit from projective geometry
>>7963904
is that website or do you mean the subject?
Dummit and Foote book Abstract Algebra. Just flip to the chapter on vector spaces and you should be all set.
>>7963840
>I'm going to be the TA of a linear algebra course this semester but i have problems for finding good problems to show
Just copy from other schools and modify them slightly. Google "Harvard Linear Algebra exercises" or something.
>>7963879
>>7963937
You can make them prove that certain families of maps are linearly independent (for example [math](x \mapsto x-\alpha)_{\alpha \in \mathbb R}[/math], [math](x \mapsto \cos(px))_{p \in \mathbb Z}[/math], etc).
You can try to find problems outside of algebra where linear algebra is useful (coupled linear recurrent sequences, systems of linear ODEs, paths in graphs)
You can try to present some basic results from more advanced classes (some very basic representation theory, Fourier analysis, projective geometry)
And of course, there are countless theoretical exercises on linear maps (a good source for these exercises are french "prepa" books, such as Gourdon's Les Maths en Tête, Algèbre, Francinou/Gianella/Taieb/Krust's Problèmes-clefs de mathématiques supérieures and Francinou/Gianella/Nicolas' Algèbre 1-3). For more computational (yet very challenging) exercises, check Prasolov's Problems and Theorems in Linear Algebra.
>>7963956
PS: if you speak a bit of french, check this website out (it is written by a first year "prépa" teacher): http://bkristof.free.fr, problem sets 15,18,23,29,30,32,33
dual space
DUAL SPACE
DUAL
U
A
L
>>7963853
delete this
>>7963974
put conguent spaces in too, it's basically the same but gives an interesting explanation of the term "congruent" as used in school
What's a good alternative to pic. related?
Need to brush up my undergrad Linear Algebra.
