Recent content by Gamble93

I realized after my post that I should have included that a non zero determinant implying linear independence is a specific case that applies to \mathbb{R}^n but I was late for class so it slipped my mind. Excuse my ignorance.

The question of linear independence of a finite amount of vectors can be thought of as asking about solutions to the equation: c_1\mathbf{v}_1+ c_2\mathbf{v}_2+...+c_n\mathbf{v}_n= \mathbf{0} where \mathbf{v}_i \in V are the vectors you are testing for linear independence and c_i \in F are...

My linear algebra instructor tried to explained to us where the vector space axioms come from. He told us that the axioms are properties of common vector spaces such as \mathbb{R}^2 or \mathbb{R}^3 that people were used to working with. Then over time people started generalizing them to...

Homework Statement Let a=p_{1}^{r_{1}}p_{2}^{r_{2}}...p_{k}^{r_{k}}, b=p_{1}^{s_{1}}p_{2}^{s_{2}}...p_{k}^{s_{k}} where p_{1},p_{2},...,p_{k} are distinct positive primes and each r_{i},s_{i} ≥ 0 Prove that (a,b)=p_{1}^{n_{1}}p_{2}^{n_{2}}...p_{k}^{n_{k}} \mbox{ where for each } i...

Thank you both for your answers. The question I posted was word for word what was on my exam. I also assumed that it was the dimension of the set he was asking for. When I get an opportunity I'll see if I can figure out the answer. Thanks again both of you.

First of all, I apologize if this is in the wrong place. I didn't really know where it should be placed and if it is in the wrong place I am sorry. This question was on my recent Linear Algebra I final exam and I had no idea how to do it when I was writing the exam and I'm still stumped by...

Nothing is wrong with infatuation. Haha. :) I did enjoy myself. I guess I'm just bitter and cynical because our break up was rather rocky. And yes, I am very glad that we never had kids, though she did try to persuade me at one point. Either way, I'm sure the OP will find someone.

I see your point DaveC. Perhaps I should have said, "What I thought was a serious relationship". I spent most of the relationship infatuated with her and spending all my money on her only to realize towards the end that she was extremely immature and was using me. Hope that clarifies.

I know how you feel. I'm your age and I've only ever had one serious relationship. In retrospect it was a waste of time because we were still in high school and she was immature. Just hold out. You'll find someone.

Haha. Well thank you. I suppose I have now been initiated?

If I were to have a fondness for a certain type of fish I guess then it would have to be the White Sturgeon.

Well, I saw another thread where the new member was warned about this. :P I personally don't like fish. Never have.

Hello. I am new to the forums. I have been, for lack of a better word, lurking these forums for about 2 months now and have decided to formally introduce myself. I have just graduated from high school and am starting my Bachelor of Science degree in September. My major is mathematics but I...