Recent content by sakodo

Hi guys, I am reading a proof on Holder's inequality. There is a line I don't understand. Here is the extract from Kolmogorov & Fomin, Introductory Real Analysis. "The proof of [Minkowski's inequality] is in turn based on Holder's inequality \sum_{k=1}^n |a_k b_k|\leq...

Regarding to your problem, Make the denominator common, apply L'hopital's rule once and after applying a trig identity you should be able to cancel out a tan(x). The answer is pretty clear afterwards. I will post a solution up if you need. Regards, sakodo

Consider the MacLaurin series for ex. ex = 1 + x + x2/2! + x3/3! + x4/4! ... Now, what do you think you need to put into x to get the alternate series in your question?

Homework Statement Let V denote a vector space of twice differentiable functions on R. Define a linear map L on V by the formula: L(u)=au''+bu'+cu Suppose that u_{1},u_{2} is a basis for the solution space of L(u)=0. Find a basis for the solution space of the fourth order equation L(L(u))=0...

Yeah is that the right term? If a matrix has a row of zeros then it has no leading terms. It was either leading term or leading column. Sorry I forgot the exact name for it.

Yeah sorry I didn't put it clearly. What I meant was x1,x2,x3 are given vectors. If the row-reduced matrix has no non-leading terms, you can deduce that the vectors are linearly independent already. Its just I don't know how to set up the proof properly lol.

Thanks for the reply Char.Limit. Assuming that x1,x2,x3 are indeed linearly independent, is my reasoning good enough? I am not sure if my proof is sufficient. Thanks.

Hi, I came across a question where I needed to prove that a set of vectors are linearly independent. The thing is, I am not sure how to reason the proof properly. Say you have three vectors x1,x2,x3 E R3, and prove that they are linearly independent. Put them into a 3x3 matrix A...

My bad.

let Det(A)=k then Det(A')=-k (two rows are switched) Det(A+A')=?

OMG I GOT IT. Since the span of S is a subspace of V, and W is the intersection of the subspaces in V that contains S, then obviously W E span{S}. Thus, span{S} E W and W E span{S} and so W=span{S}. Therefore, W is the set of finite linear combinations of S. =) Thanks so much man. You are...

Thanks for your reply vela. I get what you mean. You are saying if A is a subset of B and B is a subset of A, then A=B. Here is what I got so far: let S={\lambda_{1},\lambda_{2}...\lambda_{n}} then, A1\lambda_{1},A2\lambda_{2}...An\lambda_{n} E W1,W2,...Wm. (Closure under...

Homework Statement Let V be a vector space over the field K. a) Let {W_{k}:\ 1\leq k \leq m} be m subspaces of V, and let W be the intersection of these m subspaces. Prove that W is a subspace of V. b) Let S be any set of vectors in V, and let W be the intersection of all subspaces of V which...

Thanks, that cleared up my confusion. I was thinking that the same curve might be different in polar coordinates and cartesian coordinates lol. So when a curve is converted into polar form and plotted, the shape of the curve should still be the same right? Sorry I don't quite understand this...

Hi guys, I was trying to sketch a polar curve but my curve was different from the curve on maple(I plotted the same curve on maple). Homework Statement Here is the whole question, I am using t as theta. The hyperbolic spiral is described by the equation rt=a whenever t>0,where a is a...