Linear Definition and 1000 Threads

<Moved from a technical section and thus a template variation> 1-) Question: Let f, g and h be differentiable everywhere functions with h(1) = 2 , h'(1) = - 3 , g(2) = -1 , g'(2) = 5 , f(-1) = 4 , f'(-1) = 7. Approximate the value of function F(x) = f(g(h(x))) at point x= 1.001 2-) My...

I have the linear equation ##a + (2a - b) \sqrt{2} = 4 + \sqrt{2}##. I commonly hear that for linear equations, if we have two variables and one equation, then the system is undertermined and there are infinitely many solutions. However, how does that jive with this example, where there is one...

How do I solve this? Which of the following ordered pairs (x,y) satisfies the system of inequalities below? y>-3x+5 y≤ x-2 Choices: (2,1) (1,4) (4,1) (3,-6) Please. Thanks.

You can work a total of no more than 41 hours each week at your two jobs. Housecleaning pays \$6 per hour and your sales job pays \$9 per hour. You need to earn at least \$252 each week to pay your bills. Are the answers: x+y\le 41 6x+9y\ge252 How would you solve this? Thanks

Hi everyone! So I'm working on project where I have to design a hinge system for a hard lid that is fitted onto the back of a pickup truck. In this system, I will be using 2x linear actuator(s) that will need to lift a total weight of roughly 95kg. At the moment, I've got a selection of 600N...

ΔL=LαΔT The concept is interesting and applying its formula isn't even tedious, but what are the real factors that determine α here? I understand that thermal expansion is a direct consequence of the average separation between atoms. And that the coefficient can be found through different...

Homework Statement Find the first-order corrections to energy and the wavefunction, for a 1D harmonic oscillator which is linearly perturbed by ##H'=ax##. Homework Equations First-order correction to the energy is given by, ##E^{(1)}=\langle n|H'|n\rangle##, while first-order correction to the...

Homework Statement [ Homework Equations I found this is about linear quadrupole and these are potential of it. [/B] The Attempt at a Solution So, i solve the problem (a) by using potential. This is what I've done, I'm not sure if it is right though.[/B] And i have no idea how can i...

Homework Statement Homework EquationsThe Attempt at a Solution if there exists a set with 3 vectors, and all of them are linear independent, then by definition no linear combination of the 3 vectors can equal to 0. I believe that's an accurate definition right? So in this case, the answer...

I have two questions over linear and binary serch. 1. Homework Statement Q1: In binary search, after three comparisons have been made, only ___ of the array will be left to search. Q2: The maximum number of comparisons that a binary search function will make when searching for a value in a...

<mod note: moved to homework> Calculate the spectrum of the linear operator ##T## on ##B(\ell^1)##. $$T(x_1,x_2,x_3,\dots)=(\sum_{n=2}^\infty x_n, x_1, x_2, x_3, \dots)$$I think the way to do it is to find the point spectrums of ##T## and its adjoint ##T^*##. But I don't know how to calculate...

Let's say we have a set of eigenvectors of a certain n-square matrix. I understand why the vectors are linearly independent if each vector belongs to a distinct eigenvalue. However the set is comprised of subsets of vectors, where the vectors of each subset belong to the same eigenvalue. For...

Homework Statement Please bear with the length of this post, I'm taking it one step at a time starting with i) Let A: I → gl(n, R) be a smooth function where I ⊂ R is an interval and gl(n, R) denotes the vector space of all n × n matrices. (i) If F : I → gl(n, R) satisfies the matrix ODE F'...

Hi All, I am kind of confused at the fact that Excel uses the measurement of adjusted ## R^2 ## for simple linear regressions ; please see below. What does that even mean, what is the adjustment for?

Homework Statement Find the coordinates of each member of set S relative to B. B = {1, cos(x), cos2(x), cos3(x), cos4(x), cos5(x)} S = {1, cos(x), cos(2x), cos(3x), cos(4x), cos(5x)} I am to do this using Mathematica software. Each spanning equation will need to be sampled at six separate...

Are interpretations that are non linear with respect to the wave function (eg. GRW, transactional) compatible with string theory?

First of all I will use L to denote lambda the parameter of the distribution. X~Poission(nL), n$\in\Bbb{N}$, Y~Poisson(mL),m$\in\Bbb{N}$ with m$\ne$n S= aX+bY a,b real constants. Given observations x and y find the maximum likelihood estimator of L. The problem is I don't know what the pmf...

I have a particle that moves along a circular arc centered at origin in 2D plane. I have the following angular displacement function for time T0 through T3 and the following acceleration and velocity constraints in Cartesian coordinates. At t = T0, theta = 0, velocity = 0. At t = T3, velocity =...

kuruman submitted a new PF Insights post Frames of Reference: Linear Acceleration View Continue reading the Original PF Insights Post.

Okay here's the question: If you sell widgets for 2 dollars, you sell 300 per day. If you sell them for 4 dollars, you sell 200 per day. assume linear relat., between price (x) and # widgets sold per day (y), write linear equation relating x and y I'm thinking I plot the x,y pairs, then...

The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

http://imgur.com/a/xIydC The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D

I am taking a linear algebra class, and it has a required lab associated with it. Here is the following problem that I must solve using Matlab 1. Homework Statement Write a function using row reduction to find the inverse for any given 2x2 matrix. Name your function your initial + inv(M), the...

Hey! :o To product a product $3$ square plates $A$ with measures $300\times 500$mm and $2$ square plates $B$ with measures $400\times 600$mm are needed. These plates must be cut out by two different workpieces with measres $1000\times 1000$mm (Type I) and $600\times 1500$mm (Type II). The...

Homework Statement A bullet of mass 0.011 kg is fired at a speed of 850 m/s. It embeds itself in a man of mass 90 kg. a) Find the momentum of the bullet before it strikes the man. b) Assuming it takes 0.1 seconds for the bullet to come to rest after hitting the man, calculate the average...

I am told that the trace function tr(A) is a linear transformation. But this function maps from the space of matrices to the real numbers. How can this be a linear transformation if the set of real numbers isn't a vector space? Or is it? Can a field also be considered a vector space?

Sorry If the thread name confuse you. I want to know if I want to find the Torque from deriving Kinetic Energy and the system has Object the Rotate and the rotating cause linear motion(v). Let's say it a Rolling Disc on the non-slope plane which has angular velocity ω and that ω cause it to move...

Homework Statement A mass of 0.5 kg is suspended from a flywheel as shown in FIGURE 2. If the mass is released from rest and falls a distance of 0.5 m in 1.5 s. Mass of wheel: 3kg Outside rad. of gyration of wheel: 300mm Radius of gyration: 212mm calculate: (a) The linear acceleration of the...

Hi everyone. Excuse me for my poor English skills. I did an exam today and my exam result was 13 of 40. I don't understand why it was my result, because while doing the exam I though I was doing it well, then the result was a surprise for me. I will write down the questions and after show my...

Hi everyone. Excuse me for my poor English skills. I did an exam today and my exam result was 13 of 40. I don't understand why it was my result, because while doing the exam I though I was doing it well, then the result was a surprise for me. I will write down the questions and after write my...

Hey! :o A national economy has $3$ sectors: fishing, forestry, boat building. One fishing boat is needed, to catch two tonnes of fish. To produce four tonnes of wood, one tonne of fish is needed to feed the forestry workers. Two tonnes of wood are needed, to build one fishing boat. There...

In particular, I would like a book that explains the theory of function spaces, linear transformations, to explain the ways one can interpret ODEs as linear transformations on function spaces. I need to read up on these for a project in my Intro to Differential Equations class. Any suggestions...

Hi all, I've got this idea in my head of building a mini-loader like a http://www.multione.com/mini-articulated-loaders/ . I'm interested in replacing the hydraulics with linear actuators and wondered if anyone here could shed some thoughts/advice. Given the driveline would also be fully...

Homework Statement Let S be a set of nonzero polynomials. Prove that if no two have the same degree, then S is linearly independent. Homework EquationsThe Attempt at a Solution We will proceed by contraposition. Assume that S is a linearly dependent set. Thus there exists a linear dependence...

Homework Statement Prove that a set S of vectors is linearly independent if and only if each finite subset of S is linearly independent. Homework EquationsThe Attempt at a Solution I think that that it would be easier to prove the logically equivalent statement: Prove that a set S of vectors...

I'm trying to optimize the function below, but I'm not sure where I made a mistake. (This is an application in machine learning.)$$J(\theta)=\sum_{i=1}^n \left(\sum_{j=1}^{k}(\theta^Tx^{(i)}-y^{(i)})_j^2\right)$$ where $\theta$ is a $n$ by $k$ matrix and $x$ is a $n$ by 1 matrix...

given P(-1,1,2), Q(-3,0,4), R(3,2,1), find an equation of the line through P that is parallel to the line through Q and R. All the words after the given three points really confuse me and I just need some help on where to start to tackle this problem. Thanks

Homework Statement This is the second problem from our test preparation cycle and i partially solved and understood it. The circuit in the picture is in the state of switch being open (STATE 1: SWITCH OPEN). Calculate ##E1## so that the change in the electrical energy of the capacitor is...

Homework Statement This is one of the problem i had had some help in solving but some things remain unclear to me and i will highlight them by posting the exact question in the brackets next to the line of solution so that you can see what bothers me. Hopefully you can help me better understand...

Hey! :o Let $F$ be a field and $V,W$ finite-dimensional vector spaces over $F$. Let $f:V\rightarrow W$ a $F$-linear mapping. We have to show that $f$ is injective if and only if for each linearly independent subset $S$ of $V$ the Image $f(S)$ is linearly independent in $W$. I have done the...

Homework Statement This is the definition I got from my book: "A crucial classification of differential equations is whether they are linear or nonlinear. The ordinary differential equation ##F(t,y,y',...,y^{(n)})=0## is said to be linear if F is a linear function of the variables ##y...

AS is a local quantum field theory, so I'm assuming that it is? What do you guys think?

In an oblique collision my understanding is that linear momentum is conserved in all directions (x, y, normal, tangential). But in a constrained oblique collision, does this change? For example if we had a block lying between two frictionless surfaces with an angled face ( a slope on one face)...

Homework Statement Homework Equations N/A The Attempt at a Solution I proved the first part of the question (first quote) and got stuck in the second (second quote). I defined Im(E1) as U and Im(E2) as W and proved that v=u+w where v ∈ V, u ∈ U and w ∈ W. After that however I got stuck at...

I was reading this text where they state: "Many cosmic masers are observed to have both circular and linear polarization although the reasons for linear polarization are not well understood." Just curious, aren't there any molecules such as OH, CH4, or water masers that have transitions that...

Hello, just a quick question. I am aware that a a state in a space can be written as a linear combination of the basis kets of that space ψ = ∑ai[ψi] where ai are coefficients and [ψi] are the basis vectors. I was just wondering is this a linear superposition of states or just a linear...

Homework Statement For each of the following, determine if the system is linear. If not, clearly state why not. (a) ##y''(t)+15y'(t)+sin(y(t)))=u(t)## (b) ##y''(t)-y'(t)+3y(t)=u'(t)+u(t)## (c) ##y'(t)=u(t)## and ##z'(t)=u(t)-z(t)-y(t)## Homework Equations None The Attempt at a Solution...

I am currently brushing on my linear algebra skills when i read this For any Matrix A 1)A*At is symmetric , where At is A transpose ( sorry I tried using the super script option given in the editor and i couldn't figure it out ) 2)(A + At)/2 is symmetric Now my question is , why should it be...

Homework Statement Show that elementary row operations don't affect solutions sets in linear systems Homework Equations - The Attempt at a Solution It's pretty easy to come up with a random linear system and perform ERO on them and showing that solutions are not affected, but is there all...

Hey! :o Let $\mathbb{K}$ be a field. Find a matrix $M\in \mathbb{K}^{2\times 2}$ such that for the linear mapping $f:\mathbb{K}^2\rightarrow \mathbb{K}^2, x\mapsto Mx$ it holds that $f\neq 0$ and $f^2:=f\circ f=0$. Let $V$ be a $\mathbb{K}$-vector space and $\psi:V\rightarrow V$ be a...