Linear Algebra and Group Theory

All was going swimmingly well reading my College Physics book by Serway until the dreaded simultaneous equation which I hope somebody can help me with. I can handling them except when there are letters involved. Find 'd' I managed to get to this point then collapsed! Units have been omitted for clarity. -d sin35deg = -0.5(9.81)((d cos35deg)/25)^2 Apparently d = 108m Thanks

Hey fellas could use a hand on a linear question that has been bugging me. Give an example of a 4 x 4 matrix such that col A = nul A Appreciate any help! Thanks, ib

Can I ask why for example:- 8a^5 b^5 + 10a^5 b^5 = 18a^5 b^5 and not 18a^10 b^10 Thanks

Continuing through the algebra book I'm studying I came across this example but cannot decide if it's correct or not. Sorry but I just cannot get to grips with the proper way to present this type of equation on this forum. Hopefully it'll make sense. x^2 y^3 3z^-4 = x^2y^3z^4[/u] 3 Sorry i can't get the 3 directly underneath = x^2y^3z^4 Doesn't it work out that the 3 also comes up to the numerator? Or is it only the z^-4 that comes up if so why does the 3 stay below?

Hi, there. I have a calculation as following: BCA+B'CA'+B"CA"+... where A,B,and C are square matrices. A and B are symmetrical matrices. Since C remains the same in all the terms of this calculation, I am wondering is there a easier way to carry out this calculation, e.g. make the multiplication only once like the form of: (B+B'+B"+...)C(A+A'+A"+...) I know this form doesn't work, and it is silly to ask such a question, but just in case any one can light a light for me to some other easier forms. Thank you very much!!!

ok. i bought a business a couple of months ago. It is a service business and i have the same clients as the previous owner. He would charge a person, say $200 for the service and would have the sales tax included in that price. Well I have to pay NJ sales tax by the end of the month and am trying to find the actual base price of the service and the sales tax that would make the figure total out to $200. The previous owner would take the $200 and mulitpy it by $0.07 (nj sales tax) to come up with the sales tax to pay the government. That method is ludacris considering that he is taxing the tax that was already collected. I really suck at math but the only thing I cou…

Let u and v be any vectors in a vector space V. Prove that for any vectors xsub1 and xsub2 in V, span{xsub1, xsub2} is a subset of span { u, v} if and only if xsub1 and xsub2 are linear combinations of u and v.

Can somebody post (or direct me to) a proof/explanation that an outer product always has rank 1? Thanks!

If there are two matrices: A and B where ......0 x 0.............. 2 1 1 A = x 0 0....and B =1 2 1 ......0 0 0...............1 1 2 if the result of A*B is C: ......1 [math]\sqrt{2}[/math] 1 C = [math]\sqrt{2}[/math] 1 1 ......0 0 0 I tried many ways to figure out what the x is without success. Any one can help? Thank you.

I have not done this in a long time, and I can't for the life of me figure this out: I started out with (C - A) U (B - (A n B n C)) Is that correct? It seems I am missing something...

Dear all, Would you please give me some guidance on the following simple question? Thanks! Question description: I have a subset of vectors (1 by 3). 3 vectors will be drawn from it to construct a matrix (3*3). Of course, different matrixes will be produced if different 3 vectors are used. Some matrixes are close to singular while some are far away from singularity. My question: What rule can be used to choose 3 vectors which make the matrix far away from singularity? If the subset has 9 vectors (1*3), are there 3 best vectors which can construct a best matrix? How to find the 3 best ones?

Hi, Let [math]L/K[/math] be a simple extension : [math]L/K[/math] is a a field extension and it exits [math]x\in L[/math] such that L=K(x). I consider the endomorphism of L [math]m_x[/math] define by [math]m_x(y)=xy[/math]. My problem : I find ( and i can explain if somebody want...) that the characteristic polynomial of m_x is 0 !!! It involves that the degree of the extension is 0??? How is it possible?

Hi, I have three n*n matrices: A, B, and C. They are all real. A and B are symmetrical but C is not. M=AC+CA; and E=BM+MB. Based on the answers of the question before (the one about the M=AC+CA), I think there is no way to make M by one matrix multiplication. Thus I think the generation of E should be two matrix multiplications as well. This matrix multiplication will be carried out once for every loop of the program. Since I found the matrix C is a constant matrix for all the loops, I wonder is there a way that I can make the matrix multiplications once for all the loop, such as E=XC+CX or something like that? Thank you so much.

Is this correct? Let G be a group and H a subgroup of G. Suppose that G acts on the (non-empty) set A. Then there exists an element of A which has H as its stabilizer? The converse is easily shown. As if G acts on a set A and then pick any w belonging to A then the the stabilizer of w is a subgroup of G. I.e. it there a one-one correspondence between the subgroups of G and the stabilizers of the elements of A? Any help would be great cheer.s

Hello, I am facing a problem now. Any one can help? A and C are two real n*n matrices, while A is a symmetrical matrix and C is not. Now I need to calculate a matrix M, which satisfies M=AC+CA, on computer. Since C is not symmetrical, so far I have to use the same matrix multiplication routine twice to get the results of AC and CA, respectively. I am wondering whether there is a way that I can use the matrix multiplication routine only once and get the matrix M. Thank you a lot.

Hello, My teacher went over the proof to find the general [math]A^{-1}[/math] for 2x2 matrices. He told us that finding the general [math]A^{-1}[/math] for 3x3 matrices might take about 5 pages at least, but there's also another method that can do it in a few steps. I was wondering if anyone can provide me a link to the web page where both methods are shown step-by-step, or at least just guide me through finding the general rule if it's really lengthy to show here. Thanks

Hi all, Given two quadratic matrices A and B. Does anyone know if there exist some efficient (polynomial) algorithm for identifying subspaces that are invariant under both A and B? Thanks for help on this

Hello! I was wondering if someone can help with how Trace(AB) can be equal to Trace(BA)? Thanks!

How do I express 1/(x^4 + 1) as a partial fraction, without using imaginary numbers? I'm having trouble finding the values of a and b.

Hello, I was just curious why cramer's rule does not work for infinite solutions. My teacher said that in the class today, but he did not go into details... Can anyone please exaplin that to me... Thanks

Anyone know of a par excellence text on Linear algebra that a physics student could get?

Does anybody know of a one-one homomorphism from A4 (alternating group) into the symmetric group S6 which is not a consequence of a natural embedding of S4 into S6? Does one even exist?? AT

Can anyone help me? Let U be a subspace of R3 that coincides with the plane throuogh the origin that is perpendicular to the vector n=(1,1,1) 1. Find an orthonormal basis for U 2. Find the matrix with respect to the canonical basis on R3 of the orthogonal projection (P a linear map from R3 to R3) onto U such that range (P) = U Any help would be greatly appreciated! I dont exactly understand what to do. Thanks!!!

Galois's theorem describes the relation between subfields and Galois groups on the field. I tried to apply Galois's theorem to the relation between subspaces and automorphisms on the topological space in the following site; http://hecoaustralia.fortunecity.com/topology/topology.htm

Galois's theorem describes the relation between subfields and Galois groups. I tired to apply Galois's theorem to partially ordered set such as directed graph in the following site; http://hecoaustralia.fortunecity.com/poset/poset.htm