Linear Definition and 1000 Threads

$\textbf{10)} \\ f(x)\text{ is continuous at all } \textit{x} \\ \displaystyle f(0)=2, \, f'(0)=-3,\, f''(0)=0 $ $\text{let} \textbf{ g } \text{be a function whose derivative is given by}\\ \displaystyle g'(x)=e^{-2 x} (3f(x))+2f'(x) \text{ for all x}\\$ $\text{a) write an equation of the...

sin(x) * y''(x) + 2cos(x) * y(x) = 0 y(0) = 0 y'(0) = 1 how do I solve it? (I know the solution because I have created the diff. equation starting from a simple function). -- lightarrow

Homework Statement A particle of mass m moves along the x–axis under the influence of force ##F_x=-ax+bx^3## , where a and b are known positive constants. (a) Find, and sketch, the particle's potential energy, taking U(0) = 0 (b) Identify and classify all equilibrium points (c) Find the...

Homework Statement Show that any vector in a vector space V can be written as a linear combination of a basis set for that same space V. Homework Equations http://linear.ups.edu/html/section-VS.html We are suppose to use the 10 rules in the above link, plus the fact that if you have a lineraly...

m1v1 = m2v2 v = rω m1(rω)1 = m2(rω)2 m1ω1 = m2ω2 Does this make sense?

Homework Statement A 15 000kg loader traveling east at 20km/h turns south and travels at 25km/h. Calculate the change in the loader's a) kinetic energy b) linear momentum Homework Equations ΔKE= 1/2mvf^2 –1/2mvi^2 Δp= mv2 –mv1 m= 15000 vi = 20km/h = 5.56m/s vf= 25km/h = 6.94m/s The Attempt at...

Suppose that I have an overdetermined equation system in matrix form: Ax = b Where x and b are column vectors, and A has the same number of rows as b, and x has less rows than both. The least-squares method could be used here to obtain the best possible approximative solution. Let's call this...

Hello, I'm trying to develop a pendulum to test protective equipment so I want to work out the length I'll need to generate a desired velocity and the necessary mass I'll need for a specific moment of inertia. I know there are multiple ways to solve for linear velocity with equating Ek and Ep...

1. Homework Statement Posted Homework Equations Posted The Attempt at a Solution Posted I just need the work to be checked.

What are the best ones and why for a first-timer like myself (doing self-study)? Thanks very much everyone.

I am working on a problem that goes like this: Show that $Ker (F) \cap I am (F) = \{0\}$ if $F: W \rightarrow W$ is linear and if $F^4 = F.$ I have the solution but there is one step which I need help: (the delineation is mine) (1) Suppose that there exists $x$, such that $x \in Ker(F) \cap...

hi there,im pretty new to antenna design, still have a lot of theory to go through, so please be kind. ;)I have to design a linearly polarized microstrip patch antenna (rectangular) that is fed with 2 coaxial probe feeds. The patch should be a square (L=W), so i can place 2 feeds orthogonally...

Hi PF! The other day in class my professor mentioned something about expanding linear independent vectors, but he did not elaborate. From what I understand, if ##x_1,...,x_k## are linearly independent vectors in ##V##, where ##dimV=n>k##, how would you extend ##x_1,...x_k## to a basis ##\{...

Homework Statement Let ##C## be the space of continuous real functions on ##[0,\pi]##. With any function ##f\in C##, associate another function ##g=T(f)## defined by $$g=T(f)\equiv \int_0^\pi \cos(t-\tau) f(\tau) \, d \tau$$ a) Show ##T## is a linear transformation from ##C## to ##C##. b)What...

Homework Statement 3y(t)+2=x(t) Homework Equations k1y1(t) + k2y2(t) + 2(k1+k2) = k1x1(t)+k2x2(t) The Attempt at a Solution I know the system is non linear but I cannot explain why. It has something to do with 2(k1+k2) but I am unsure.

I'm looking at purchasing Algebra (2nd Edition) by Michael Artin, is this a good book to purchase as my first intro to linear algebra book for self learning?

1.) Two volumes of an encyclopedia stand side by side, in order, on a shelf. A bookworm starts at page i of Volume I and bores its way in a straight line to the last page of Volume II. Each cover is 1 mm thick, and the first volume is 2/5 as thick as the second volume. The first volume is 40 mm...

Homework Statement Find the general solution for the DE: t2y''-2y=0 Homework Equations These were given for other parts of the problem so I'm not sure if they're relevant. y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7 The Attempt at a Solution The t2 at the front was really stumping me and I'm not...

I was given a question relating centripetal force to solve A linear spring of negligible mass requires a force of 18.0 N to cause its length to increase by 1.0 cm. A sphere of mass 75.0 g is attached to one end of the spring. The distance between the centre of the sphere M and the other end P of...

So anyone of you know a book that provides a gentle and quick refresher for linear algera, in the spirit of the book "Quick Calculus" by Kleppner and Ramsey? Now that I am studying quantum mechanics, I feel I need to review the linear algebra I studied during my engineering degree. Thanks.

Hi all, I have a question regarding a simple crank and slider mechanism, but I'm not a mathematician. This means that long formulas scare me... (: I've been searching around and haven't found anything I can really understand. I'm trying to get a "ball park" formula to calculate the amount of...

Homework Statement Hi, Just watching Susskind's quantum mechanics lecture notes, I have a couple of questions from his third lecture: Homework Equations [/B] 1) At 25:20 he says that ## <A|\hat{H}|A>=<A|\hat{H}|A>^*## [1] ##<=>## ##<B|\hat{H}|A>=<A|\hat{H}|B>^*=## [2] where ##A## and ##B##...

Homework Statement A semi-circle of radius R has a charge Q uniformly distributed over its length, which provides a line charge density λ. Determine E at the origin. Homework EquationsThe Attempt at a Solution https://www.physicsforums.com/attachments/105239 I can tell by argument of...

<1 and <2 form a linear pair. If m<1 = 5x + 9 and m<2 = 3x + 11, find the measures of both angles.

May I start by saying hello to all and that I have visited the site before, but have yet to create an account until now. With that said, I am having difficulty calculating proper numbers for a project I am designing. Mind you, it has been about seven years since I was in any physics or...

Homework Statement Construct a subset of the x-y plane R2 that is (a) closed under vector addition and subtraction, but not scalar multiplication. Hint: Starting with u and v, add and subtract for (a). Try cu and cv Homework Equations vector addition, subtraction and multiplication The...

I have the following linear differential equations: ##A\dot{x} + By = 0## ##C\dot{y} + Dx = 0## Where x and y are functions of t, and A through D are constants. I can solve this fairly easily by differentiating the first equation, rearranging, and removing one of the variables, which gives me a...

So many moons ago I made myself a pretty bog standard dual linear bench power supply using an LM317 and LM337 to give me -15 - 0 - +15. In an attempt to get more current out of it (for no real reason other than because I can) I got a larger transformer and a beefier rectifier, then using the...

This is a linear algebra question which I am confused. 1. Homework Statement Prove that "if the union of two subspaces of ##V## is a subspace of ##V##, then one of the subspaces is contained in the other". The Attempt at a Solution Suppose ##U##, ##W## are subspaces of ##V##. ##U \cup W##...

Homework Statement The Attempt at a Solution \left[ \begin{array}{cccc} 1 & 0 & 5 & 2 \\ -2 & 1 & -6 & -1 \\ 0 & 2 & 8 & 6 \end{array} \right] \sim \left[ \begin{array}{cccc} 1 & 0 & 5 & 2 \\ 0 & 1 & 4 & 3 \\ 0 & 0 & 0 & 0 \end{array} \right] From the RREF it is...

hello :-) here is my problem...: 1. Homework Statement For a linear harmonic oscillator, \hat{H} = \frac{\hat{p}^2}{2m} + \frac{1}{2} m \omega^2x^2 a) show that the expectation values for position, \bar{x}, and momentum \bar{p} oscillate around zero with angular frequency \omega. Hint...

the answer key said d is supposed to be 10. but there's a way to evade that row exchange. 1st picture is the question and the 2nd picture is the elimination steps.

I used to know this back when i worked with Flash animation, but I'm working on a 3D printer now and I've forgotten, when you have a set of teeth, on a linear shaft and a gear, do you base the unrolling of the gear, for the spacing, on the inside of the teeth, the outside of the teeth, or the...

Hi. I have read many times that the Schrodinger equation is a linear equation and so if Ψ1 and Ψ2 are both solutions to the equation then so is Ψ1 + Ψ2. Is this use of the word linear the same as generally used for differential equations ? As the Schrodinger equation is also an eigenvalue...

http://<img src="https://latex.codecogs.com/gif.latex?L_{2}[0,1]->L_{2}[0,1]\int_{0}^{1}\left&space;|t-s&space;\right&space;|f(s)ds" title="L_{2}[0,1]->L_{2}[0,1]\int_{0}^{1}\left |t-s \right |f(s)ds" />[/PLAIN] I have many doubts on linear operator. How I can find a spectrum of a linear...

Homework Statement Consider the four vectors (1, 1, 1), (2, −1, 3), (1, 7, −1) and (1, 4, 0). Calculate how many ways you can write (1, 1, 1) as a linear combination of the other three, explaining your reasoning. The Attempt at a Solution wouldn't any of these combinations give the correct...

Homework Statement Let be E a normded vectoriel space, ##dim(E) = m \in \mathbb{N}^{*}##, I have to show that ##\exists \rho_{1}, \rho_{2} > 0 | \forall u \in L(E), ||u^{m} - Id| \leq \rho_{1} \Rightarrow |u - Id| \leq \rho_{2}##. Homework Equations Nothing. The Attempt at a Solution [/B] I...

According to Pauli principle the two fermions can not occupy one state of a Hamiltonian. Can the two fermions occupy a state which is linear recombination of two states of the Hamiltonian?

I collected data on a periodic mechanical motion. The amplitude is damped linearly. What mathematical function models linear amplitude decay. All I can find is exponential decay of a sine wave.

Hello, I just completed a first course in linear algebra and really enjoyed my studies. So much so that I want to pursue it more in the fall as an independent study, i am a EE major in college and was curious what directions might be useful for applications in that field.

Hello! I'm trying to derive the linear velocity vector from the position vector and the angular momentum vector. I've seen on the internet that V = W x R (V,W and R are all vectors and x is the cross product) but I cannot for the life of me derive it! I've tried doing it by writing out the...

Homework Statement I'm reading through the derivations of the linear wave equation. I'm following everything, except the passage I highlighted in yellow in the below attachment: Homework Equations I'm not understanding why partials must be used because "we evaluate this tangent at a...

Hi folks, I have just found a video on youtube that shows how a 2 mile linear accelerator was built in 1967, I share it with you, hopefully you will enjoy it as much as I did:

I have reading through various sources on linear functionals, but all seem somewhat inconsistent with regard to denoting the set of all linear functionals and the set Also, what is the standard definition of a continuous linear functional? I really couldn't find much besides this Let ##f : V...

Homework Statement A uniform thin stick of mass M and length L has a moment of inertia about its centre of mass of I = (1/12)ML^2. The stick, which is pivoted at one end, is held horizontal and then released. Assuming the pivot is frictionless, calculate: i) the linear acceleration of the free...

If you were to perform a linear regression of log10(B) vs log10(x) what would you expect the slope to be? The expected relationship between B and x is B(x) = μoI(2πx)-1

Homework Statement Refer to figure. Homework Equations v=ds/dt → ds=vdt a=dv/dt → dv=adt ads=vdv The Attempt at a Solution I tried taking the derivative of the given position function. Then I am kind of lost from there.

I have two table, first one changes quadratically and second table changes linearly. 46 ... 55 90 ... 57 142 ... 59 202 ... 61 270 ... 63 346 ... 65 430 ... 67 522 ... 69 622 ... 71 730 ... 73 846 ... 75 970 ... 77 and so...

Homework Statement Let T be a Linear Transformation defined on R4 ---> R4 Is that true that the following is always true ? KerT + ImT = R4Homework EquationsThe Attempt at a Solution Since every vector in R4 must be either in KerT or the ImT, so the addition of those subspace contains R. and ofc...

I derived a relation between the product of two linear polynomials and the square of their average. It can be used to solve any quadratic equation. Will this help me getting into a top university?