Linear Algebra and Group Theory

Sorry, guys, this isn't abstract but the calc board didn't seem very active... I could really use the help on this one... Prove: f(x): [a, b] ----> R has f'(x) continuous @ each x in [a,b] then the definite integral from a to b exists Could someone please make a proof for this one? I am lost as to what to do.

can somebody pls help me figure this problem out?? f : Z SUB 7 --> Z SUB 7, f([n] SUB 7) = [2n] SUB 7 is this one below correct?? f : R --> R, f(x) = 2x + 1 f'(x) = 2 > 0 and f(x) = 2x + 1 passes the horizontal line test so f is 1 to 1 but how do I figure out if it is onto?? is this one correct below?? f : Z -->Z, f(n) = 2n + 1 f'(n)= 2 > 0 and f(n) = 2n + 1 passes the horizontal line test so f is 1 to 1 but how do I figure out if it is onto?? thank you

how do u express a determinant of a sum or two matrices in terms of determinant of each matrix?

Question: Let G be a permutation group on the finite group omega. Suppose IGI = power of p, where p is a prime. Prove that IFix(G)I = IomegaI under mod p. (I am using IGI to denote the order of G) I know this has something to do with orbits and stabilizers. I also know how to get as far as the all Fix(G) are inside the center. But that is where I can't figure out how to go any further.

The question goes like this: Determine all cyclic groups that have exactly two generators? I know that the answer is, Z, Z3, Z4, and Z6... however, I don't understand where that comes from, how do you know those are the only ones? Why isn't U(10) one? My test is tomorrow, I would really appreciate your help!!!

Hi, I have the following problem: Consider the infinite strip pattern: ... TTTTTT ... Prove that every element of the symmetry group of the above pattern has the form t^n or (t^n)r where t is a suitable translation and r is a suitable reflection. Is this group Abelian? I can see clearly why every element of the symmetry group has either of those forms, basically just because every isometry can be proven to be either a translation, a reflection, a rotation or a glide reflection and clearly neither a glide reflection nor a rotation will yield symmetry. Then clearly we take t to be the translation 'one unit' to the right or left and then r as a reflection thr…

Let N = 8765^4321 be writen in decimal notation. If A is the sum of the digits of N and B is the sum of the digits of A, then what is the sum of the digits of B? Have Fun.

While trying to teach myself a little quantum mechanics in the evenings, I came across the following sequence of formula's and text. Although the subject is quantum mechanics, the question I have is a mathematical one. [math]\int_{-\infty}^{+\infty}dx\psi_m(x)\psi_n(x)=\delta_{mn}[/math] these functions form a complete set [math]\sum_{n=1}^{\infty}\psi_n(x)-\psi_n(x')=\delta(x-x')[/math] The question I have is: are both statements required for the set of [math]\psi_n(x)[/math] to be complete ? Or which of both is sufficient ? Greetz, Leo

did modular addition and multiplication today in my proofs II class and i was wondering if there are modular set products. I was thinking since mod operations create equivilance classes, which are sets, if there were an special things to do with mod set products or if they even exist.

Im as is to see, quite new to this forum, and i was wondering where to ask questions about transition equasions (dont know if ive got the right word, still have to get a scientific dictionary) the reason im asking it here is because it is mathematics, but its just because most normal electronics formulas dont aply, and the fact that it sometimes involves complex numbers (j) example of what i mean: ive got an analog butterworth filter to the first degree, I just need to know the amplification factor formula, which is voltage_in(Uin)/voltage_out(Uuit)=H(w) where w is the frequency of the voltage, (the variable so to say) ive got to: Uin-Uuit((1-(1+jwrc))jw2rc+1…

Hi ya. can anyone give me a hint on how to start showing the following :For any artitary subsets of R 1)a complement of a complement is the original set 2)complement of a union is the intersection of the complements. cheers.

1)Let G be an Abelian group and let H={g in G/ IgI divides 12}. Prove that H is a subgroup of G. Is there anything special about 12 here? Would your proof be valid if 12 were replaced by some other positive integer? State the general result? 2) Find a collection of distint subgroup <a1>, <a2>,.....,<an> of Z240 with the proberty that <a1> C <a2> C.....C <an> with n as large as possible. if you have time, drop me a line anyone!!!

had an idea in class the the other day...feel free to add on or modify for whatever, just a rabbit trail of thought.... Let A = { pi , 2^(1/2) } A only contains 2 items and so Card(A) = 2 => there exists a bijective function from A to the natural numbers of order 2 => A is finite...probably didnt need to prove it but there it is. Write the items in A as sets themselfs as such pi = {3, 1, 4, 1, 5, 9, ... } 2^(1/2) = { 1, 4, 1, 4, 2, 1, ... } So can A be rewritten as A = { {3 1 4 1 5 9...} , {1 4 1 4 2 1...} } ? Would this imply that A has an infinite number of things dispite that it is a finite set? Or is it just my notation and how i'm def…

First of all, I'd like to say Hello to everyone as this is my first post Now the fun part, I spend 2-3h in painful strugle and I was unable to prove the following question. If anyone knows how to solve it it will be largely appreciated Prove for any positive integer n that: 2196^n – 25^n – 180^n + 13^n is divisible by 2004 Have Fun

In a group, prove that (ab)^-1=b^-1a^-1. Find an example thats hows that it is possible to have (ab)-2=/=b^-2a^-2 Find distinct monidentity element a and b from a non-Abelian group with the property that (ab)-1=a^-1b^-1. Draw an analogy between the statement (ab)^-1=b^-1a^-1 and the act of putting on and taking off your sock and shoes (shock and shoes property). anyone help pls!

Hello! I've worked on a problem concerning even and odd numbers recently...sounds quite simple actually...though I'm not sure whether my (more or less formal) solution is right. It is asked to find out whether there are more even or odd numbers...The result I came to is that there is an equal number of them...How would you solve this problem?

I've got an exercise I would like to discuss with you...I came to this idea because of the thread "even and odd numbers" which has a lot to do with it... Task (Source: V.A. Zorich, Mathematical Analysis 1, Springer-Verlag): a) Prove the equipollence of the closed interval [math]\{x\in\mathbb{R}~|~0\le{x}\le{1}\}[/math] and the open interval [math]\{x\in\mathbb{R}~|~0<x<1\}[/math] of the real line [math]\mathbb{R}[/math] both using the Schröder-Bernstein theorem and by direct exhibition of a suitable bijection. b) Analyze the following proof of the Schröder-Bernstein theorem: [math](card~X\le{card~Y})\wedge(card~Y\le{card~X}) \Rightarrow (card~X=card~Y)[…

-------------------------------------------------------------------------------- These questions are relative to Equivalence Relations.... Question[1]..Let S be the set of real number. If a,b exist in S, define a~b if a-b is an interger. Show that ~is an equivalence relation on S. Describe the equivalence classes of S. Question[2]... Let S be the set of intergers. If a,b exist in S, define aRb if ab>=0. Is R an equivalence relation on S? Question[3].. Let S be the set of interfers. If a,b exist in S, define aRb if a+b is even. Prove that R is an equivalence relation and determine the equivalence classes of S. Hints: 1]..(a,a) exist in R for all a ex…

Bottle caps that are pried off typically have 22 ridges around the rim. Find the symmetry group of such a cap. Please help me this problem, thanks a lot!

I took a Discrete Math class two years ago. Let me tell you, completely worthless. I never understood how it counted as "Math". The first three chapters didn't even use numbers. The section I took was for computer science, but the material hardly seemed relevant to programming, or at least not the programs I created. Is Discrete Math COMPLETELY WORTHLESS, or are there some obscure uses for this garbage?

There has been much talk of late of a Russian mathematician(Dr. Perelman) 'proving' the Poincare conjecture. For those of you who don't know it and are curious check google, as it is a one of the biggest problem in maths, that has been round for 100 years or so, and will take much too long to explain in detail here. For those of you who are familiar with it and the supposed proof adopted using Ricci flow and 'snipping' the singularities, does it appear to you to be more of a quick fix approach than a rigorous mathematical proof. For instance at what point does one decide where to clip the singularities? Is it an arbitrarily defined point? Isn't the inclusion of disclu…

this problem is due on wedd. , i hope you guys will help me out with this.... In the cut "As" from Songs in the Key of Life, Stevie Wonder mentions the equation 8 x 8 x 8 x 8 = 4. Find all integers n for which this statement is true, molulo n. thanks alot for your help......

does [math]-log_ax = y \Longrightarrow a^{-y} = x[/math] or [math]\Longrightarrow -a^y = x[/math]

how would you go about solving [math]log_3x - 2log_x3 = 1[/math]

The highest mathematics training i have had is Algebra II in high school. I need help extracting some equations for this thread: http://www.scienceforums.net/forums/showthread.php?p=66913#post66913 . If someone could teach me how to or do it for me, it would be apprecciated.