Independent Definition and 745 Threads

Homework Statement Let A = \left[\begin{array}{ccccc} 2&0&-2&1&-3 \\ 1&1&-3&0&-2\\1&0&-1&-1&3 \end{array}\right] a) Find two linearly independent vectors u and v in R5 such that span{u,v}={x \in R^5 : Ax=0}. b) Find three linearly independent vectors u,v and w such that col(A) =...

hi guys, can a time independent system model be controlled via a controller? I am assuming that we can obtain a solution for the model at each sample time, just assume that the model is of c= a*u type, i.e u is input which varing with the time. I am confsed...

Homework Statement determine whether the following are linear independent sets of vectors in the vector space R*R of all functions from R to R a)fn:=1+t+...+t^n for n=1,...4 b) sin,sin^2 ,sin^3 c)1,sin^2,cos^2 Homework Equations The Attempt at a Solution can i do like this for...

There are a wealth of resources... videos, texts, libraries, etc. that are available to us in our studies in physics. Even Physics Forums sections devoted to compiling lists of such resources! For the sake of pacing, discipline, and other reasons (guidance?), who else would be interested in...

I was wondering, if you are told that for two events A and B, We Have P(A)=0.4 and $P(A\mid B) = 0.4$\\ Can you assume as P(A) = P(A\mid B) That these events are independent? regards Brendan

Hi, I'm a bit stuck on this problem A basketball player misses 30% of his free throws. He ends up in a situation where he has the potential to shoot two penalty shots if and only if he lands the first shot (called a one and one, I believe). The outcome of the 2nd shot is independent of the...

Hello all, I am working on this problem, have searched my textbook, this forum, etc and am still as lost. I suspect I need to (in some form) use the formula P(AB)/P(B) = P(A) as it is the integral formula of this section. Any suggestions or hints are greatly appreciated. A fair coin is...

Homework Statement Let u_1...u_n be linearly independent column vectors in R^n and A an invertible n x n matrix. Prove that the vectors Au_1...Au_n are linearly independent. Homework Equations The Attempt at a Solution It is easy to prove this using scalars and the definition of...

Homework Statement When are the vectors (1,x) and (1,y) linearly independent in R^2? When are the vectors (1,x,x^2), (1,y,y^2), and (1,z,z^2) linearly independent? Generalize to R^n. The Attempt at a Solution At first, I think I misconstrued the question and I ended up finding basis...

Homework Statement Let V = {differentiable f:R -> R}, a vector space over R. Take g1,g2,g3 in V where g1(x) = e^{}x, g2(x) = e^{}2x and g3(x) = e^{}3x. Show that g1, g2 and g3 are distinct.Homework Equations If g1-g3 are linearly independent, it means that for any constant, k in F (field) then...

I'm doing a lab where i need to calculate the heat energy, or enthalpy using the equation (delta) H = m x c x T my reactions are going to be of a strong acid and a strong base: Sulfuric Acid + Sodium Hydroxide→ Sodium Sulfate + Water and of a wek acid and the same strong base...

Given random variables X and Y, which are not independent, is it always possible to find a random variable W which is independent from X, such that Y = f(X,W), for some function f? Example: let the joint distribution of X and Y be Y 0 1 X+------- 0|1/3 1/6 1|1/6 1/3 Then if we...

I have 1000 experiments on the same data, each of which is trying to decide the probability that the data agrees with a model. The problem is, even if each experiment REALLY agrees with the model (ie. p(d1) = .99, p(d2) = .99, etc), when I multiply these together to get P(d1 & d2 & d3... &...

Homework Statement Assume that H0 describes a paramagnetic system that couples to a magnetic field via the Zeeman effect, i.e. V = −μB, where μ is the magnetic moment. Note that for the unperturbed paramagnetic system the probability of having an up-spin is equal to that for a down-spin. Show...

Einstein wrote ... Q: What would happen inre (in regards to) time if, for any reason, a clock were to be 'independent of the state of motion of [its] body of reference'? A: _____ (?)

Homework Statement Given vectors: a1 = (1; 2; 0), a2 = (2; 1; 3), a3 = (0; 3; -3). Find out if these vectors are linearly independent. Homework Equations The Attempt at a Solution \begin{cases}...

If you have a 3x3 matrix AB of rank 2, and you are asked to find two linearly independent vectors in the column space of A, are those the same vectors in the column space of AB? I figure it is since if the vectors are linearly independent they wouldn't change. Am I right?

Can two independent sources of light be coherent?

Hi guys, I am solving a problem in the form: (ATx=0 where A is a matrix of known numbers and I am solving for x. After performing reduction and multiplying ATx, I am left with the following equations: -X1 + X4 - X5 = 0 -X2 + X4 = 0 -X3 + X4 -X5 + 28X6 = 0 From these equations, I...

What kind of knowledge do independent invent0rs have? Do they have knowledge in all the areas of engineering? Thanks!

I'm looking to do a guided independent study course at my college next term; the college doesn't offer physics beyond the introductory calculus-based sequence, which I've completed, and I'm not yet ready to transfer. The physics major sequence at the school to which I intend to transfer...

Hi everyone, I know this subject has been broached before but would appreciate some extra help - I'm an English major in second year uni so I haven't done physics and maths for a while, but I have quite a lot of free time at the moment and would really love to get back into these subjects...

Homework Statement If the current density is time independent and divergence free, show that the Maxwell Equations separate into independent equations for \vec{E} and \vec{B}. Homework Equations Maxwell's equations The Attempt at a Solution The only Maxwell equation with \vec{j}...

So the question is... Let v1, v2,...,,vn be linearly independent vectors in a vector space V. Show that v2,...,vn cannot span V. I honestly have found myself completely lost lately and I suck at writing proofs. So this is what I see, v1, v2,..., vn is linearly independent iff...

I would appreciate some help with this problem. Assuming X and Y are independent, I'm trying to find the correlation between XY and Y in terms of the means and standard deviations of X and Y. I'm not sure how to simplify cov(XY,Y)=E(XYY)-E(XY)E(Y) =E(XY^2)-E(X)E(Y)^2. If X and Y are...

\varepsilon _t = z_t \sigma _t z_t \sim IID\,N\left( {0,1} \right) \sigma _t^2 = f\left( {\sigma _{t - 1} ,z_{t - 1} } \right) Are the epsilons independent from each other? Why?

If nuclear forces would be spin independent! HI all,a question was asked by my teacher that "if nuclear forces would be spin independent then how many types of DEUTRON would be existing and what would be their relative abundances. Please help Thanks

I am in a senior level scientific measurements using digital interfacing class, which is basically like a smash-up of digital circuits lab, intro to DAQ and DAC/ADC, and senior project. Now, part of this class, only 10%, is a independent "research" project. I put this in quotes because we only...

I was just doing some revision and came across a sticky thought - Suppose you got two appraisers for 9 car damages and both give different prices for the repair. Would the samples be independent or paired? I reckon it's paired but I can't put a reasoning behind it! And I also did a 95%...

Hi I am supposed to, without calculation, find 2 linearly independent eigenvectors and a eigenvalue of the following matrix A 5 5 5 5 5 5 5 5 5 The eigenvalue is easy -- it is 15. And I can find one eigenvector, [1 1 1] (written vertically), but another without calculation? Is there...

Hi. Gauss' law applied to gravity states that the gravitational flux through a given surface is proportional to the total enclosed mass. Considering a gaussian surface which encloses a continuous mass distribution, an arbitrary re-distribution of the total mass must yield the same value...

Hi, Is there any trick to treat complex conjugate variables in polynomial equations as independent variables by adding some other constraint equation ? Say, we have polynomial equation $f(x,x^{*},y,...) = 0$. where x^{*} is the complex conjugate of variable $x$. I might think of taking $x = r...

1. Homework Statement Find two linearly independent solutions valid for x>0 xy''+y=02. Homework Equations well first of all, all the solutions that i get to see in the forums is interms of the euler formula.. but in the course that I am taking(advanced engineering mathematics), it is...

i got these question which i do not know how to do... Qn. In a forced mechanical oscillator, show that the following are frequency independent. i) the mechanical amplitude at low frequencies. ii) the velocity amplitude at velocity resonance. iii) the acceleration amplitude at high...

Q: If X_1 and X_2 are independent exponential random variables with respective parameters \lambda_1 and \lambda_2, find the distribution of Z = X_1 / X_2. Discussion The best method to attack this problem apparent to me is coming up with a cumulative distributive function for Z and then...

Hi, I'm trying to work out a probability value from a number of distributions (tests), it gets a little complicated because some of the tests are dependent on each other. Lets say I have a surface which has black and white regions distributed over it, where black is "true" and white is "false"...

It's very commong to use z and z* as two independent variables, differentiating with respect to one while keeping the other constant. Can you please give me some intuitive insight into this method, and why it works so well? Because every time I see this my first thought is that z and z* are NOT...

Hi everyone, I was reading about Gram-Schmidt process of converting two linearly independent vectors into orthogonal basis. But, as I understand, if two vectors are linearly independent then they are orthogonal! isn't that right?? Could anybody explain... please.

Hello everyone, summer break has begun for me, and I was wondering which way is the best possible way to learn new stuff over the summer, I wanted to dive into, and kind of begin, to have an understanding of Lorentz Transformations and Einstein's special relativity theory, is there any book or...

Homework Statement For indices running from 0-3: R_{iklm} = -R_{kilm} = -R_{ikml} With the above conditions how do I know the number of independent component is reduced from 4^4 = 256 to 36. No idea how to figure this out.

This probably has a really simple answer. Forr u=x^2-y^2 and v=x^2+y^2 x and y are apparently the dependent variables. But the independent variable is the input while the dependent variable is the output, so since u=f1(x,y) and v=f2(x,y) shouldn't they (u and v) be the dependent variables?

Hi wondering if can anyone help me... I've gotten so bogged down in all the rules and stuff for singular/non-singular matrices I've completely confused myself! Can anyone tell me is it true to say that if I have a matrix P, det(P) is NOT EQUAL to 0, then the vectors that would form the...

Why is it that we can treat electrons as independent and non-interacting in solid state physics? What is the difference between mean-field theory and density functional theory? In lame terms please.

Homework Statement Determine whether the given vector functions are linearly dependent or independent on the interval (-\infty, \infty) \begin{pmatrix} t \\ 3 \end{pmatrix}, \begin{pmatrix} 4 \\ 1 \end{pmatrix}Homework Equations The Attempt at a Solution I computed the wronskian to be t-12...

Looks like I will not have any research opportunities this summer. However , could I conduct my own research indepedently without working in a professor's research group?

Hi Suppose X_{1}, \ldots, X_{n} is a sequence of i.i.d. random variables. We define X_{(n)} = max(X_{1}, \ldots, X_{n}) X_{(1)} = min(X_{1}, \ldots, X_{n}) Are X_{(n)} and X_{(1)} independent? Whats the best/easiest way to verify this? Thanks Vivek

For two independent and identically distributed random variables having the exponential distribution, do they have the same lambda value, or are the lambda values different?

A solution to time dependent SE but not Time independent SE?? How is it possible that a wave function is a solution to the time dependent schroedinger equation, but not to the time independent schroedinger equation (without time factors tacked on) with the same potential? I had this case on my...

Proof: 1. why you need at least m vectors to span a space of dimension m. 2. If m vectors span an m-dimensional space, then they form a basis of the space.

Homework Statement http://ocw.mit.edu/NR/rdonlyres/Physics/8-044Spring-2004/7A20B047-A049-44D6-96D2-75602F179856/0/notes_dfnitns.pdf There it says tht the number of independent variables of a simple fluid is 2 (see the "Complete Specification" section). But the ideal gas law is PV=NkT which...