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...

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...