Hello everyone! I have never used this chat; I do not know how it works here. So I just post a little questionchen and somebody will answer or do I need something special?
@Kasmir: You have to ask where you can expand it in a series. The series you wrote down (centered at $0$) converges only on $|z|<1$. But you can expand it (and you should know how to do this) in a series centered at $z=2$ or $z=i$ or ... any $z=z_0$ with $z_0\ne 1$.
Probably too much hassle for just a month or two. But why not just gather kids you know are interested and do some math after school? You might talk to a teacher about it.
@Kasmir: Everywhere? And do you know how to do it, say at $z=2$?
@Ted heh, so i sent an email to the mathcamp people a few days ago, when i was considering applying about financial aid. they said financial aid is flexible and that we wouldnt have to pay the whole fee in the case we can't afford it
Hi ! I'm been proving some theorems on linear algebra and I stumble upon one that I dont understand. It says if $A$ is a matrix m x n with $m < n$, then $AX = 0$ has at least one non trivial solution. I get that if $m < n$, and if we name $r$ to the non null rows then $ r \le m$ then $ r < n$, and here it says as $ r < n $ we know it has at least one non trivial solution, why ? Is it because I have a variable dependent of the others ?
In English, @Maks, we say there have to be free variables because there are too many columns. That means you'll have parameters in your answer, so infinitely many answers.
Note that because you're looking at $AX=0$, rather than $AX=b$, the system is consistent — i.e., has solution(s).
With a $b$ there it might be inconsistent — i.e., have no solution.
My desk right now has: 2 phones, a raspberry pi computer, my math notebook, a bunch of supplies like compass and ruler, fortune cookie wrapper, 22 guage wire, colored pencils, the art project, and of course my computer
@TedShifrin really? i dont have one lying around tonight. will check tomorrow. I always thought that is where I picked this notion up when I first learned topology
