Linear Algebra and Group Theory

Which is a faster method, I don't know how to do matrices so I can't compare the two personally.

Cycling is not a sort of breakdown that the Simplex algorithm occasionally does, but the sign of the existence of extraordinary solutions that assign positive values to more than $m$ decision-variables, where $m$ is the number of our structural constraints. Simplex, by its very nature, cannot find such solutions but is able to emit a signal of their existence by cycling. Consider the classical example given by E. M. L. Beale\footnote{The coefficient of $x_{5}$ on the objective function is altered slightly for reasons that will soon be understood.} where $n=7$ and $m=3$ [see Bazaraa et al., p.176]: \[ \left. \begin{array}{lrrrrrrrr} max. & & …

https://en.m.wikipedia.org/wiki/Draughts Can Draughts or Checkers game played between two opponents be designed and developed using a 5*5,7*7,9*9,11*11 board ? I.e Odd number of sides. Thanks & Regards, Prashant S Akerkar

For example: (1) 3x + 2y + 7z = 100 (2) 21x + 3y - 5z = 50 (3) 4x - 2y + 3z = 20 What is the algebraic method to solve for the sum of unknown variable equaling the number of equations. So if I had 5 unknown variables and 5 equations that included those 5 unknown variables and so on and so on This was my method using a different equation: Isolate x from (1) sub into (2) Isolate y Sub y into x next sub x and y into (3) Isolate z And it worked.

The reason I ask is because I am doing Circuit Analysis and the guy uses Matrices to solve for the variables. I think he just wants me to buy the other other tutorial on Matrices that's why he introduce them into Circuit Analysis... Anyway since it is solving for unknown variables (I did some high school algebra but that is it) can you use algebra substitution method instead of using a matrix/matrices to solve for unknown variables. I have not learnt Matrices yet.

Hello All, I have 2 identical triangles in different places and need to know the rotation and movement to get from triangle #1 to triangle #2. There is no perpendicular angle in that triangle(s). the rotation has to be in quaternions. The movement in x=x+/-n y=y+/-n z=z+/-n I am coding in Java3d but any other language would work for me to understand how to do that. Any help is much appreciated! Thanks, Duesentrieb

How we can derive the general equation of the circle? X square + Y square + 2gx + 2fy + c = 0 Thanks & Regards, Prashant S Akerkar

Excuse my ignorance, but with an equation like this; 32 x 0.5x = 1 is there a formula I can use to calculate the index number x ? cheerz GIAN

Does anyone know what this is, understand it, and can explain it to me? Please...

I've never quite accepted the Axiom of Choice and have heard some others don't either. This is how I now think of it: For example, suppose you were going to play in a doubles tennis match and you were given a group of 50 people to choose your one partner from. You may have no idea of how good any of them are so you choose one at random. You are given the right or privilege by the Axiom of choice , but it doesn't tell you which one to choose. It's possible you may know which ones are the best yourself, but the Axiom of choice doesn't pick one for you. This could be repeated multiple times; you could be presented with many different sizes of groups or sets. The Axiom of cho…

How Linear Algebra Used in the field of computer science ???? Tell me Some Applications please

I am self learning and trying to solve the above problem. I have no clew how to solve it. Any hints how to proceed? I am planning to use Taylor series will it help me?

is the function x²+3 surjective for real numbers. how do you test for surjectivity in general?

For matrices, if AB=I, then does that mean BA=I also? If I have 2 matrices and I have AB=I, is that sufficient to conclude that B is the inverse of A? Or do I have to calculate BA explicitly too? I've tried finding a simple 2x2 counterexample but I can't find any. All examples of AB which I've conjured up also have BA=I.

Hello guys! I've faced a minor difficulty in proving the statement "√3 is irrational number". My arguments are the following: Let's suppose that √3 is rational then it can be expressed as p/q, p,q∊Z which is irreducible, so √3=p/q <=> 3=p2/q2 <=> p2=3q2 And here is a problem from p2=3q2 I concluded that p=3a, a∊Z after that the proof is led to contradiction => p/q can be reduced by 3. The ground for my doubt is we cannot conclude from product's divisibility the divisibility of it's factors (maybe even these factors are the same) e.g. 12 | 3*8 but 12 ∤ 3 and 12 ∤ 8. I apologize for my English)) and appreciate any attention.

It would suprise me to no degree if this topic has already been discussed, but I would like to know if there are any proven correlations between pi, phi, and eulers constant? If anyone could help me with this I would be much obliged.

i study alone and i'm having difficulties with these issues, please help me! Questions: 1- Determine which type of central grid is from its curves. (X ^ 2) / (a ^ 2) + (y ^ 2) / (b ^ 2) - (z ^ 2) / (c ^ 2) = -1 2- Prove that rotations in R ^ 2 commute. Ra * Rb = Rb * Ra 3- Prove that roca in R ^ 3 do not commute. 4- How to transform cylindrical coordinates into Cartesian coordinates? 5- ρ sin ϕ = 2 A surface in R ^ 3 is given by coordinate (ρ, θ, ϕ), how to translate into Cartesian coordinates and what is this surface?

I got another math team packet, this is in the advanced math section, i.e., Trig and Calculus, but I still want to know how to do it. So lets see, I need to solve the Quadratic for all values of X. The equation is |x| = x2+x-3=0. So I see that is in Quadratic form. So I get the coefficients of the variables, plus the -3 at the end(ax2+bx+c=0) So a = 1, b = 1, and c = -3. So I plug that into the Quadratic Formula. This gets me to: [math]/frac{-1 \pm \sqrt13 }{2} = |x|[/math] So |x| = -1 +- sqr(13)/2 The Math Drawer isn't really working... Don't know were to go now

Do you tell me about pythagorean theorem? What scientist thinks about this? And how can I find the appropriate triangles?

I have to find out whether two 3d shapes which are standard mathematical ones.I dint need the solution but i only need ,is there a common solution or not.Am i wrong Comparing collision with Common solution?

Hi, I have a system of equations with 3 unknowns, the coefficients are shown as a matrix below, and wondered if this would be a good way to solve for the variables? 2270 -1800 0 | 15 -1800 3480 -680 | 0 0 -680 1150 | -8 I'd like to calculate all the steps manually, but all the matrix examples i've seen so far seem to use much simpler, single digit numbers, so what i'm trying to ask in a roundabout way is; do numbers this size lend themselves to a matrix, or is their a better way to solve? Thanks for looking, and any help is much appreciated.

Hi, I'm trying to get some insight on the concept of Fields. Definitions abound on the net, and i think i have a clear picture of them. I'd like to know if my following interrelated ideas are correct: (1) A polynomial is a field. (2) A set of polynomials is a field Now i think (2) creates more possibilities for discovery, and maybe it is even the correct way to go if one talks about Fields, whereas (1) is more restricted in that the coëfficiënt-space and power space are smaller; or 1-dimensional maybe, So, if i see a polynomial, i see a Field because the four operations are defined (the "sum" of monomials where then the monomials are a "product")…

Hi there, I haven't been on here for almost a decade but I was wondering if someone could have some ideas on a binary (ternary would can also be acceptable) , discrete metric which is intransitive, that is fully, not partly, i.e. for all x,y,z: xRy ^ yRz => !(xRz). I see various ideas in topologies which are not dense and so on but it must be a discrete metric function. I been brainstorming for a good while but I can't quite come up with a solid solution, so ideas are very welcome.

Hi. I'm looking through this book: https://www.math.columbia.edu/~woit/QM/qmbook.pdf At the very top of page 8, the following is presented: g1 . (g2 . f)(x) = g2 . f(g1^-1 . x) = f(g2^-1 . (g1^-1 .x)) = ... I understand what they did - they applied equation 1.3 from the previous page treating g1 as g in 1.3 and then applied 1.3 again treating g2 as g. But it looks to me like it would also be valid to do this: g1 . (g2 . f)(x) = g1 . [ (g2 . f)(x) ] = g1 . [ f(g2^-1 . x) ] In other words, it looks like we can great f as a function acted on by group member g2, and move g2 inside first, OR treat g2 . …

Hello all! It's been quite a while since I posted here. I noticed this question while trying to help a niece solve a piece of homework and I just couldn't figure this one out. This isn't homework for me, trust me, I have left school long ago. Could someone enlighten me as to the solution for this one and how to go about solving them? Just in case I need to assist with homework again in the future... at least then I'll be able to provide pointers. I also hate not being able to answer such things. I had initially attempted to treat it as a simultaneous equation but I'm not convinced that it's the correct way to handle this one. Thanks!