Linear Algebra and Group Theory

what's the proof for the discriminant [math]b^2-4ac[/math]? e.g. Proove that if [math]b^2 > 4ac[/math] then x has 2 real and distinct roots.

We all know how to diagonalise matrices. But ever since i leanrt how to I was like WTF do u use it for???? Until now, the only really useful application is to write any general quadratic form as a sum of perfect squares. Any of you guys know any?

My theorum : A continuous fraction can be defined as an infintisimal bound progressivly by a scaling speciffic infinty; and thus be represented as 2 equations instead of a division. Proof : -We are going to examine the equation (1/3) -draw a number line from 0 to 1 - solve the equation for 1 decimal point (you should get 0.3). You now know the answer is between 0.3 and 0.4. -draw 2 lines at 0.3 and 0.4 : Try to be as accurate as possible -shade between the lines -draw another number line from 0 to 1, identical to and directly below the first one - solve the equation for 2 decimal points (you should get 0.33). You now know the answer is between 0…

Which solving method do you use? and Which ones do you know? A mexican invented one method named DGO but i want to know if you know it already, because if not, i can explain it here.

how do i show that |AB| = |A||B| ?

x^3 - 4x^2 - 25 has a factor (x-a). Find the value of a. I've tried two methods for this. The first one basically went f(a)= a^3 - 4x^2 - 25 = 0 SQRT(a^3 - 4x^2 - 25) = 0 a^(3/2) - 2x - 5 = 0 dunno where to go from there. The other method i tried was something like x^3 - 4x^2 - 25 = (x-a)(bx^2 + cx + d) = bx^3 + cx^2 + dx - abx^2 -acx -ad = bx^3 + (c-ab)x^2 + (d-ac)x -ad Equate coeffecients: b = 1 c-ab = -4 c-a(1) = -4 c-a = -4 d-ac = 0 …

I would like to know the following: Let kappa be a regular cardinal and B a kappa-club (kappa-closed and cofinal in kappa). And let lambda be another regular cardinal strictly smaller than kappa. Why is it possible to choose a strictly increasing sequence {alpha_nu : nu < lambda} in B, such that the suppremum of {alpha_nu : nu < lambda} has cofinality lambda ? My first guess would be to use the fact that for every nu < lambda and every non empty A subseteq B intersection nu, sup A an element of B is. And then do something with transfinite recursion, but why would B even contain any ordinals smaller then lambda ? I hope someone could shed some light …

hi, this question is about quadratic programming, and im trying to formulate this problem, but having no luck with it, the problem is: A company produces 2 types of products A and B, it costs the company £40 to make product a and £70 to make product B. from research it is suggested that if the seeling price of A and B are set as c and D then they will sell x of A and Y of B, given by the realtionship: c = £220 - 3x and d = £250-2y. How would i formulate this problem to give me the answer as: max: -3x^2-2y^2+180x+180y. Please help

I've been thinking about a new type of encryption, really an older type of encryption, but with a twist. Standard public key systems are fairly secure, but one of the ways to break them is to brute force the private key, either the pass phrase or the number itself. This would be impossible if a two layer key system was established. It would have to be set up so that key one generates coded output based only on the key it recieves first. This new coded output would then be decoded to plain text with the next key. Obviously then, the bruteforcing algorithem would not detect any plain text, even if it succesfully cracked the first phrase, so the message could never be decode…

heh I was reading about that last month or so, when I drifted off topic. Here's the site i was reading: http://mathforum.org/isaac/problems/prime1.html Most notably: As far as your question goes, I'm not really sure, but I suppose the theorem implies something . I hope that site helps. As for the avatar? blike said it had something to do w/ the forum shift. :/

When i type out 0! on my calculater it gives an answer of 1, does anyone know why that is? I would have expected it to be 0

:phi: = 1.618... uh... something like that, i don't remember So what do you guys think about this number? It appears mysteriously in nature in the most unexpected places. The leaves on plants base their "spiral" arrangement up the stem on this number. also, any number in the Fibonacci sequence divided by the preceding number in the sequence will approximately equal :phi: Fibonacci Sequence: 1,1,2,3,5,8,13,21,34,55,89... 1/1 = 1.000 2/1 = 2.000 3/2 = 1.500 5/3 = 1.667 8/5 = 1.600 13/8 = 1.625 21/13 = 1.615 . . . 89/55 = 1.618 This converges to :phi: There's some more crazy characteristics to this number…

When i inquired to my professors, they were at first a little negligent to answer but eventually came to say that when using natural systems, like we typically do in orgo chem, natural log is much like an average that we use.... yet i still dont see the relationship. for example, if i type in LN 5, i get something like 1.609.... if i use LN 6 ill get another number... LN 7 etc.. but if i graph the line, its not linear by any means which explains why its not proportionate either. What purpose does performing LN 5 do? Also, what purpose does this have when im using LN to determine graphically Ea of a reaction?

How would i find 0.5 in (mod 7)? - i don't want the answer, but a few hints on how i would do it. All i know about mod is that in programming, it gives the remainder when a number is divided by another number, but from what i've been reading, i think that it has a different meaning in this context. From what i've been reading on the internet, it seems that in (mod 7), numbers would go 0, 1, 2, 3, 4, 5, 6, 7 and then start again - is that right? Would that mean that 0.5 in (mod 7) would still be 0.5 since it is between 0 and 7?

Can anyone prove this? If Tau(n) is an odd integer, then n is a perfect squre Thanks, Austin

it looks like this particular forum hasn't had many posts in general, which i think is a shame considering that the topic of it (fractals and chaos theory) is such an interesting and diverse topic. so, i decided to write my own mandelbrot set generator, even though there are hundreds around i suppose, and i've included the source code which is available here. you'll need a linux machine to compile and run the program, but a Makefile is included. You'll also the need the png and gd libraries and header files for gd. program usage: ./mandelbrot x1 x2 y1 y2 width iterations/pixel it's a fairly simple program to use. the mandelbrot set is defined in the complex pl…

I am enrolled in Linear Algebra this coming semester. Has anyone had any experience in it? Any advice?

hello, i'm studying vectors, and i have come across spanning, linear independency and bases. i have two bases in v3® which are 1) (1,0,0) , (0,1,0) , (0,0,1) 2) (1,0,3) , (2,1,4) , (1,0,0) i have shown these to be linearly independent as this is one of the points that must be met for a base to occur. The second point is to show that they are spans of their own set, for this i know they must have some linear combination. This is the bit that is confusing me, how can i show the linear combinations, basically how do i prove the second point of having a base. Any ideas?

hi, im doing stuff on the gemetrical objects in the subspaces of v3® and v4®, and how they are represented. i'm confused as i don't understand how i am supposed to show this. can someone please help me!!! Thanks

When 1 is added to the numerator and the denominator of the fraction m/n the new fraction is 3/2. When one is subtracted from the numerator and denominator of the fraction m^2/n^2 the new fraction is 21/8. Find the possible values of m and n. The values i get for n and m are surds, but the answer is apparently m=8 and n=5, which do work. I wont post my working cos i'm pretty sure i'm totally off track. Any help plz?

does anyone here know anything about clock mathematics? I have come across it a few times, and it seems simple enough; rather than the numbers being on a line, they are on a ring, like a clock is 1-2-3-4-5-6-7-8-9-10-11-12 so when we are at 10 on a 12 hour clock, and we add 4 (hours), then the time we get is not 14, but 2, and so on. I believe this is used in encryption, and for solutions to elliptic equations (and probably other things now that wiles solved fermat's theorem) however I was wondering about this, has anyone done this before: instead of numbering from 0 or 1 to n, how about numbering from -n to 0 or -1 (depending on if you want a zero or not.…

Can you arrange the digits 1,2,3,4,5,6,7,8,9 in an order so that the number formed by the first number formed by the first 2 digits is divisible by 2. First 3 digits divisible by 3. First four digits is divisible by 4 and the first 5 digits is divisible by 5 and so on up to nine digits? 12 is divisible by 2, 123 is divisible by 3, 1236 is divisible by 4, 12365 is divisible by 5, 123654 is divisible by 6 but 1236549 is not divided by 7! i hope you can help thankz!

Numbers, why is everyone so stereotypical about thhem. They say 3 "always" comes after 2 and before 4. But why? Isn't it mean to assume that three is always there? I mean, girls got mad when guys were stereotypical about them, why should they be mean to numbers? Numbers have feelings too you know! ____________________________________________________ I did this as a joke, but please still reply as if I'm serious.

hi can anyone here help me solve this???

Is it just me, or is this whole imaginary number stuff just a bunch of crap? I learned this in Algebra II class the other week. Now, my teacher is trying to apply it. What meaning will this have in my life? Don't get me wrong, I understand the concept...but, why do I need to know this?