Independent Definition and 745 Threads

Ok. Sooo. Let's say u have y=x+5. Then u know y-5=x. Now if u have y=x^2 - x. How would u rearrange it to find out what x equals. I found out that in general I cannot rearrange ewquatioms with mitiplr x variables with different exponents. So help me please

Homework Statement if v_1,v_2,...,v_k be k linear independent vector, and if v_1,v_2,...v_k,v be k+1 linear dependent vector, then v is the linear combination of v_1,v_2,...,v_k Homework Equations n/a The Attempt at a Solution some of my attempt,(direct proof) v_1,v_2,...v_k,v be k+1...

Homework Statement If v11,...,vk,v are linear independent, prove that v\notin \left\langlev1,...,vk\right\rangle Homework Equations n/a The Attempt at a Solution i can prove it by contrapositive, but I'm curious how to proof it with "If v11,...,vk,v are linear...

A quote from the book of T.L. Chow 'Mathematical methods for physicists' The reader may notice that dy/dx has been treated as if it were a ratio of dy and dx, that can be manipulated independently. Mathematicians may be unhappy about this treatment. But, if necessary, we can justify it by...

Homework Statement Let \Omega=\{HH,HT,TH,TT\} and let F and U be two partitions of \Omega: F=\{G,K\} with G=\{HH,TT\} and K= \Omega\backslash G, while U=\{V,W\} where V=\{HH,TH\} and W= \Omega\backslash V. If 2^\Omega is the \sigma-algebra of \Omega, and A=2^F and B=2^U...

Should be simple, but can't figure out :) Why is that , for a field K, the linear independence of field homomorphisms g1, ..., gn: K -> K equivalent to the existence of elements a1, ..., an \in K such that the determinant det| gi(aj)| != 0 (...so, just like in a case of linear...

du/dt = d2u/dx2 u(x,t) = (t^a) * (g(e)) where e = x/sqrt(t) and a is a constant Show that integral from -inf to inf [ u(x,t) ] dx = integral from -inf to inf [ (t^a) * g(e) ] dx is independent of t only if a=-0.5 My attempt was to diff both sides by t (sorry not x) giving integral from...

Hi, Is this differential equation valid for time independent acceleration" a = dV/dt = dV/ (V dx) = ( dV / dx ) * (1/V) ?

I understand the Michelson–Morley experiment and its result; but what I don't know yet is the REASON. Example: A torch in free space is moving at a velocity [v] w.r.t me. Considering the material nature of light, shouldn't the speed of photons emitted from the torch be [v+c] w.r.t ME? According...

thanks everyone I found an answer

Hey, I go to the University of Rochester, and I am currently entering my sophomore year as a physics major. Speaking to one of the physics department's staff members at the school, I was able to set up a research position with one of the professors in the astrophysics department. In order for...

Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the...

Hi All I was re-reading the first pages of the book from Mr Claude Cohen-Tannoudji ,... (Quantum Mechanics) and something called my attention. In commenting the appearence , in 1905, of the photon notion in Albert Einstein's paper on photelectric effect, he (Mr. Claude) says that only in...

Hi all Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable? Thanks Tim

I've looked it up and can't really find a clear answer.. For a system of 3 simultaneous linear equations, is there any difference between 'the equations are linearly independent' and 'the equations have a unique solution'. If so what is it? Thanks!

Homework Statement This is really a maths problem I'm having. I need to get the general solution for the infinite square well in the form: u = A cos(kx) + B sin(kx) I found the general solution to be: u = A exp(ikx) + B exp(-ikx) Using Euler's formula: exp(ikx) =...

For (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) let Xk = [∑(from i=1 to k) Yi] / [∑(from i=1 to k+1) Yi] where k = 1,2,3 How can I prove X = (X1, X2, X3) is independent? What I did was... (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) = (Z1, Z2, Z3, Z4) / (Z1+Z2+Z3+Z4+Z5) where Z ~ N(0,1), Z IID G(1/2) Now...

I still can't visualise them. They deliver the same current all the time, however there is no potential drop across them. Is it just a theoretical device that doesn't exit? I am sure current sources do not add new charge into the circuit, but rather move charges around but this requires a...

Say I have an urn containing a set of balls numbered 1 through N. I then make n selections from the urn with replacement. Thus each selection is independent. Let the event: A_{i} i=1,2,3...,N be that the ball numbered i was not chosen in the n selections. Then...

Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!

Homework Statement V = { (x_{1},x_{2},x_{3},x_{4},x_{5}) \in R^{5} : x_{1} -2x_{2} + 3x_{3} - x_{4} + 2x_{5} = 0 } show that S = { (0,1,1,1,0) } is a linearly independent subset of V. The Attempt at a Solution I don't get it.. it's a set with 1 non zero vector, it's going to be...

Homework Statement Let \{ X(t),t \ge 0\} be a random process with stationary independent increments and assume that X(0)=0 . Show that: E[X(t)] = {\mu _1}t Homework Equations The Attempt at a Solution I tried to work backwards by argueing that the mean between time...

Homework Statement Let X and Y be independent and normal, then we know that It must be the case that X+Y and X are jointly normal Therefore we can apply the projection theorem: which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-\rho^2VAR(B) , apply the theorem to A=X+Y, B=Y...

I can understand that if z= a + ib then z*=a - ib, where the definition of the complex conjugate is reversing the sign in front of the imaginary part. I'm now confused about how the complex conjugate works in the TISE. in a stationary state, i\hbar\frac{\partial\Psi}{\partial\\t}= E\Psi...

Vector and matrices...are the independent or dependent Homework Statement Determine whether the vectors v1=[1,-1;0,0],v2=[2,-2;1,... and v3=[-5,5;1,0] are independent or dependent. Find the span {v1,v2,v3} and give a description. Explain why W = [4,4;4,4,] is not in the span {v1,v2,v3}...

Homework Statement Determine whether the vector v1=(!,2,3),v2(3,2,1) and v3(1,1,1) are independent or dependent. Homework Equations I'm so lost The Attempt at a Solution I'm so lost

Hi, everyone: I was reviewing some intro material, and I ended up confused with the issue of independence with the following problem: We are given two teams, A,B, playing against each other. A wins with probability P(A)=0.6 , B wins with P(B)=0.4 (games are played until...

I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have...

Number of "independent" subcubes of a hypercube Hello, I am trying to solve this problem: I have an n-dimensional hypercube and m of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that: - each subcube from the set may contain only those m...

Homework Statement Let S be the sample space for rolling a single die. Let A={1,2,3,4}, B={2,3,4}, and C={3,4,5}. Which of the pairs (A,B), (A,C), and (B,C) is independent? Homework Equations P(A|B)=P(A) P(A|B)=P(A&B)/P(B) P(A&B)=P(A)*P(B) The Attempt at a Solution P(A)=2/3...

Homework Statement Hi there, I'm doing a practical investigation to see how the centripetal force required for circular motion varies with the frequency of rotation, and I was just wondering which is the independent variable, and which is the dependent one. The investigation involves...

Homework Statement Suppose that A, B, and C are not linearly independent. Then show how the \alpha_{i} can be computed, up to a common factor, from the scalar products of these vectors with each other. Hint: Suppose that there are non-zero values of the \alpha_{i}'s that satisfy...

Homework Statement So I'm trying to find a basis for the space that is spanned by the given vectors. {(1,0,0,1) (-2,1,-1,1) (6,-1,2,-1) (5,-3,3,-4) (0,3,-1,1)} These are written as column vectors. Homework Equations None really (that I know of) The Attempt at a Solution So I...

Homework Statement Were the columns of A linearly independent? The matrix A is given in row reduced echeleon form 1 2 0 0 0 0 1 0 0 0 0 1 Homework Equations Hint: Consider the solution set to A x = 0 The Attempt at a Solution I think that the...

Let x1, x2,...,xk be linear independent vectors in a vector space V. If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain. By deleting a vector from linearly independent span, the other vectors, I believe, will remain...

Let x1, x2,...,xk be linear independent vectors in a vector space V. If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain. By deleting a vector from linearly independent span, the other vectors will remain independent...

In short, I think I may want to spend either next semester or all of next year at the Independent University of Moscow, but I've only really decided this recently. I haven't spoken to my university, asked for recommendations yet, or filled out the application form, and all of this must be...

Homework Statement Two cards are drawn from a standard deck with replacement. A=first card is an ace. B=second card is an ace. Show that A and B are independent Homework Equations P(A and B)=P(A given B)/P(B) P(A given B)=P(A) The Attempt at a Solution P(A)=4/52 P(B) =4/52 P(A...

Say I have a packet of electrons just sitting there, before they repel each other, what is their potential energy? I have no idea of how to calculate their potential energy since at r = 0 , U = infinity, which is not helpful since my problem requires U to be finite but the only way I know of...

Standard Matrix for R^3 -> R^4 where if domain is Linearly Independent so is codomain Homework Statement 5. Suppose T : R^3 -> R^4 is a linear transformation with the following property: For any linearly independent vectors v_1, v_2 and v_3 in R^3, the images T(v_1), T(v_2) and T(v_3) are...

Homework Statement Among all independent vector sets in a vector space U, let M = {v1, v2, ... vp} be an independent set. p is as large as it can get. Show that U is a basis of M. Homework Equations The Attempt at a Solution If U is a basis of M then U is an independent set (we...

What is it meant by "mass-independent renormalization scheme"? Does it mean that the counter-terms that cancel the infinities do not have dimensions of mass? In this case, any regularization scheme not involving the cutoff method, such as dimensional regularization? Or does it mean that...

Say I want to parametrize the plane. I can use cartesian (x,y) or polar (r,theta). But I cannot use x and r, because if I draw a circle and a vertical line, there are two points of intersection. I guess x and theta will do, because theta specifies a ray that will intersect any vertical line...

Hi, I am attempting a logistic regression analysis with a binary response and explanatory variables measured at the individual level and also some measured within subgroups of the observations (nests). For each nest containing individual observations I know the distribution of income in the...

why use non parametric mann-whitney U test rather than parametric independent sample test. I have a question regarding this because i just complete two question, as one I am using parametric tests, independent sample test, solve the mean selling price of a home with a conservatory different...

Is there any physical reason why second order approximation to ground state in time independent perturbation theory is always negative. I know how to prove it mathematicly but I wonder whether one may justify it using only physical arguments.

I am currently a senior in high school and I am working towards a career which involves the study of physics. I am somewhat aware of independent research opportunities for high school students in other areas of science, but I do not know of any opportunities which I could explore for physics...

Through our research we discover that an AC induction motor can act as a DC amplifier, as long as there is torque making it turns. Applying the process we are able to build RPM independent grid tie induction generator. Tested with variable US grid at consumer configuration. Similar to PMA...

Hello, I'm using UV-C (Hg low pressure lamp) and I wanted to see if someone could give me some insight. I have a couple of questions: 1) How far does UV-C penetrate through various materials? In my testing, it seems to go straight through plastics. I have UV blocking glasses - but those are...

Let X1, X2, ...Xn be independent exponential variables having a common parameter gamma. Determine the distribution of min(X1,X2, ...Xn). The Attempt at a Solution I know how to do it with one X and one parameter but I am at a loss with these multiple ones... Thanks so much!