Linear Definition and 1000 Threads

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?

Dx (t)=(B u (t) - v (t))dt B is 7x3 which is known U is 3x1 unknown V is 7x1 which is known dt is step size 0.1 A matrix is equal zero How to design a controller that will drive state to zero

So I am currently learning some regression techniques for my research and have been reading a text that describes linear regression in terms of basis functions. I got linear basis functions down and no exactly how to get there because I saw this a lot in my undergrad basically, in matrix...

Homework Statement Let P be the set of (x,y,z)^t in R^3, which satisfies the following inequalities: -2x+y+z <=4 x-2y+z<=1 2x+2y-z<=5 x>=1 y>=2 z>=3 Homework Equations I want to find the vector in the set with the maximal length. The Attempt at a Solution I have transformed the linear...

Hello guys, since linear motors are too expensive I decided to buy a rotational motor and use some gears and a crank mechanism to get enough torque and translate rotation into linear motion. I need to meet a certain force on the shaft though. The question is how do I calculate the resulting...

Homework Statement If n is a positive integer, then 2x2 matrix [-32,252] [-4,32] raised to the power of n is... Homework Equations I know that first I should diagonalize the given matrix, something I also seem to have a hard time with. The Attempt at a Solution I determined the eigenvalues...

Homework Statement Find the matrix that represents a rotation counterclockwise around the origin by 75 degrees followed by a reflection about the x-axis Homework Equations I know that for A rotated counter clockwise you use the 2x2 matirx [cos(theta), -sin(theta)] [sin(theta, cos(theta)] and...

Current schedule: Summer: Elective Fall: -not important, but it can't be changed in any way- Spring: Differential Eqs., Classical Mechanics & Mathematical Methods 1 (Physics), Linear Algebra, Chemistry Lab, Elective I'm thinking that since the spring schedule looks kinda heavy I can switch up...

I am stuck with the concept of linearising the non-linear system...what i thought was...non-linear systems are defined by differential equations which is difficult to solve, hence we linearise them to make the differential equation look like a algebraic equation...am i right ?...or is there...

Homework Statement Homework EquationsThe Attempt at a Solution So the general solution is the sum of the null solution (Yn) and particular solution (Yp) I believe I just need to write: y = e2t + 5e8t - 5 + C and then find the derivative of both sides y' = 2e2t + 40e8t is this correct?

Jackson discussed two center-fed linear antenna: once at page 412 (section 9.2) the other at page 416 (section 9.4) I just cannot figure out what are the difference? I though they are different method of calculation but (9.56) is different from (9.28).

Good Evening Everyone, A group of friends and I were having a mini-contest, to see who could theoretically make anti-matter using the most simplistic design in terms of cost and general complexity. The obvious choice for us was the Positron, due to low energy requirements on all fronts. One of...

I have a trouble with ODE, I try to find asymptotic solution for odes which presented in pics. But I can’t. Please introduce a method which I solve these equations. I can solve these equations analytically but after solution, inverse Laplace transform must apply to find final answer. In...

Homework Statement T:R2[x] --> R4[x] T(f(x)) = (x^3-x)f(x^2) Homework EquationsThe Attempt at a Solution Let f(x) and g(x) be two functions in R2[x]. T(f(x) + g(x)) = T(f+g(x)) = (x^3-x)(f+g)(x^2) = (x^3-x)f(x^2) + (x^3-x)g(x^2) = T(f(x)) + T(g(x)). let a be scalar in R: aT(f(x)) =...

Mod note: Changed thread title from "exponential vs linear function" to "quadratic vs linear function. basic question, won't give the full question as i don't need it solved for me, but rather need a conceptual overview of HOW to solve so i can do it myself given two functions A f(n)= c * n B...

Homework Statement Under what restrictions on ##c, d, e##, will the combinations ##c\vec u + d\vec v + e\vec w## fill in the dashed triangle? Homework Equations The Attempt at a Solution Clearly, ##\vec w + a (\vec v - \vec w) + b(\vec u - \vec v)## will be in the triangle when ##0 \leq b...

Where can I find one of these? That is, are there linear actuators where I can specify the force it should apply and it gives me back exactly how much force was applied? Are there any linear actuators that can do this and also give me position feedback, i.e., where my object is after it has been...

Homework Statement truck moves oils (lubricating oil presumably) to gas stations. At full load the truck transportation cost is 300$ when the traveling distance is 120km and the transportation cost is 350$ when the traveling distance is 165km At this interval, the costs change linearly. You...

Homework Statement Suppose that pairs of vectors ##v_1, v_2## and ##v_1, v_3## and ##v_2, v_3## are linearly independent. Must ##v_1, v_2, v_3## be linearly independent? Homework Equations So this means ##v_1 \neq av_2##, ##v_1 \neq bv_3## and ##v_2 \neq cv_3## The Attempt at a Solution For...

I am encountering a difficult(atleast to me) mathematical problem? I need to calculate the impact of a formulae on two sets of data for two different years Consider for example I have a simple formulae A * B * C * D = F where A,B,C,D are 4 parameters that affect the value of F. Now I have a 2...

'Homework Statement Find the matrix A' for T: R2-->R2, where T(x1, x2) = (2x1 - 2x2, -x1 + 3x2), relative to the basis B' {(1, 0), (1, 1)}. Homework Equations B' = {(1, 0), (1, 0)} so B'-1 = {(1, -1), (0, 1)}. The Attempt at a Solution I'm confused at what exactly a transform matrix...

Homework Statement In regards to linearization of a nonlinear system in differential equations. What does it mean for a linear approximation to be reliable to describe the long term behavior of the non-linear system around the equilibrium point? Homework Equations jacobian matrix The Attempt...

I was wondering if there was anyone comfortable enough about basic to advanced linear algebra concepts who would be willing to participate in a chat/whiteboard based platform to discuss or answer questions concerning such concepts. I need clarification on a few things

consider the two vectors v1 = (3i, 2), v2 = (-3, 2i). in C^2 Above C we get, v1 * i = v2, therefore they are dependent. Now above R, we can't see that they are dependent. Why if i take the determinant of those vectors i get get 0 |v1 v2| = 2x2 matrix = 0 ( which means two column vectors are...

Homework Statement Homework Equations The Attempt at a Solution [/B] Back again :) Is this correct? Thanks.

Hi, I stumbled upon thinking that "Is curl operator a linear operator" ? I was reading EM Theory and studied that the electromagnetic field satisfies the curl relations of E and B. But if the operator was not linear then how can a non linear operator give rise to a linear solution. Thus it...

Is there a difference between the following statement "The number of dimes is 5 times more than twice the number of nickels" and "The number of dimes is 5 more than twice number of nickels"? The 5 times more... and the 5 more than... confuses me. Please clarify this for me. Thanks!

Homework Statement check for linear dependecy[/B] f(x) = cosx and g(x) = xcosx 2 functions from R to R Homework EquationsThe Attempt at a Solution Why this is wrong: if i take the scalar a1 = 3, a2 = 1 i can do that since 3 is real, and a1 is in R. so 3f(3) + -1g(3) = 0 there for we have none...

Functions f,g from R to R. f(x) = xcosx, g(x) = cosx for x = 0, we get f(x) = 0, g(x) = 1. so for scalar t in R t(f(x)) + 0 * g(x) = 0 . ==> f(x) and g(x) are linearly idepenent. Is that right? if so in functions we search for an x that makes the function dependent?