Linear Definition and 1000 Threads

Homework Statement Find the values of k so that each of the following systems in unknowns x, y, and z has (i) a unique solution, (ii) no solution, (iii) an infinite number of solutions. x + y = kz = 1 x + ky + z = 1 kx + y + z = 1 Homework EquationsThe Attempt at a Solution I really don't...

Homework Statement Determine whether of not each system has a nonzero solution. x + 3y - 2z = 0 2x - 3y + z = 0 3x - 2y + 2z = 0 Homework EquationsThe Attempt at a Solution Using a ti-84 I put the matrix in rref and I get a nonzero solution for x and y and zero for z but when I find the...

Hello all. After completing a problem in which we derived the formulas for potential and spring force energy as functions of time, with simple harmonic motion I noticed the equations are EXACTLY the same, but with sine and cosine switched. The equations were: A sin^2(pi * t) A cos^2(pi * t) I...

Hi PF! Generally speaking, how would one solve $$f''-a(x) f = 0 : f(0)=0,f'(0)=1$$ Or if you could point me to a source that would be awesome too!

So, my linear algebra book, if you can call it that, says the following: $Ax=b$ is a system of linear equations with $m$ equations and $n$ variables. ${v}_{1}, {v}_{2}, ..., {v}_{n}$ are the vectors in the columns of $A$. The following are equivalent: (1) The system $Ax=b$ is possible for...

Homework Statement Find Green's function of ##u''+u=f##. Homework Equations What we all know. The Attempt at a Solution Let Greens function be ##G##. Then ##G''+G=\delta(x-x_0)##. This admits solutions superimposed of sine and cosine. Let's split the function at ##x=x_0##. Then we require...

Homework Statement I have data for the count rate (of gamma rays) against the thickness of various materials (Al, Pb, Fe etc...). I want to work out the linear attenuation coefficient. Can I do this by plotting the natural log of count rate against thickness? I don't have values for...

How can I classify a given first order partial differential equations? Are all first order linear PDEs hyperbolic? Quora Link:https://www.quora.com/How-do-I-classify-first-order-PDE-elliptic-hyperbolic-or-parabolic-using-method-of-characteristics

Homework Statement I have an assignment for my linear algebra class, that I simply cannot figure out. Its going to be hard to follow the template of the forum, as its a rather simply problem. It is as follows: Given the following subspace (F = reals and complex) and the "linear image"...

Homework Statement "A ball thrown straight up with an initial speed of 30/m/s. (a) Show the time it takes to reach its trajectory will be 3m/s (b) Show that it will reach a height of 45m" Homework Equations h=ut+1/2g^2 1/2gt^2 The Attempt at a Solution Part a of the question I am fine with...

Hi All, This is probably trivial. What is the difference between techniques such as Linear/Logistic Regression, others done in ML , when they are done in Standard software packages : Excel ( incl. add-ons ), SPSS, etc? Why use ML algorithms when the same can be accomplished with standard...

Homework Statement For the first question , why when the humidity increase by 1 percent , the moisture content will increase by 0.2727 percent ? Shouldn't it the moisture content will increase by 0.2727 + 0.4911 percent when the humidity increase by 1 percent ? Second question , it's clear that...

When we consider representation of the O(1,3) we divide the representation up into the connected part of SO(1,3) which we then extend by adding in the discrete transformations P and T. However, while (as far as I know) we always demand that the SO(1,3) and P be represented as linear operators...

How can the "end effect " be reduced on a long Bar magnet where the (for example) North pole is along the length of the top side. For example a 0.5 cm square bar say 5" long is stuck (South) onto a metal backing. The center length of 4" has a linear field effect but the ends have a bloom...

##f(x,y)## a critical point is given by ##f_x=0## and ##f_y=0## simultaneously. the test is: ##D=f_{xx}f_{yy}-(f_{xy})^2 ## if ##D >0 ## and ##f_{xx} <0 ## it is a max if ##D >0 ## and ##f_{xx} >0 ## it is a min ##D >0 ## is is a saddle if ##D =0 ## it is inconclusive, and ##f_x## and...

Hi, I read that linear combinations of a state, Psi, can be as: \begin{equation} \Psi = \alpha \psi + \beta \psi \end{equation} where ##\alpha## and ##\beta## are arbitrary constants. Can however this be a valid linear combination?\begin{equation} \Psi = \alpha \psi \times \beta \psi...

My formal education in Linear Algebra was lacking, so I have been studying that subject lately, especially the subject of Linear Independence. I'm looking for functions that would qualify as measures of linear independence. Specifically, given a real-valued vector space V of finite dimension...

Homework Statement A ball with moment of intertia bmr^2 rolls without slipping down a plane inclined at angle O. What is it’s linear acceleration? Homework Equations Fnet= ma T = F x r T = IO’’ a = rO’’ The Attempt at a Solution Fnet = mgcos(O) - FfT = FfrT = IO’’ Ffr = bmr^2O’’ Ff =...

Homework Statement Solve the system of equations: { (1/2)x-y=3 and x=6+2y Homework Equations NA The Attempt at a Solution The solution is 3=3, which is an identity, which means that there is an infinite amount of solutions to the system. Here's where my question lies (asked my teacher but...

I got the following two integral for the a particular solution of a 2nd order linear ODE $$(D-a)(D-b)y = g(x)$$ by using inverse operators ##\frac{1}{D-a}## and ##\frac{1}{D-b}##. The two different integrals are obtained by operating these operators in different order on y to get a particular...

Hi, This looked interesting. Determinant and Linear-Algebraic aspects of Sudoku puzzles: http://www.student.montefiore.ulg.ac.be/~merciadri/docs/papers/sudoku.pdf

From wikipedia: "An electromagnetic wave such as light consists of a coupled oscillating electric field and magnetic field which are always perpendicular; by convention, the "polarization" of electromagnetic waves refers to the direction of the electric field." A polarizer is an object that...

I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe...

Homework Statement Let ##T:ℝ^3→ℝ^2## be the linear transformation defined by ##\begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix}\mapsto \begin{bmatrix} x_1 + x_2 + x_3\\ 0 \end{bmatrix}##. i. Find the standard matrix for ##T##. Homework EquationsThe Attempt at a Solution For this problem I was...

[FONT=verdana]Dear Every Body, I need some help. First question: Is the tension of the string is the same or different? A pulley of moment of inertia 2.7 kg [FONT=&quot]· m2 is mounted on a wall as shown in the following figure. Light strings are wrapped around two circumferences of the pulley...

Homework Statement Construct a 3 × 3 example of a linear system that has 9 different coefficients on the left hand side but rows 2 and 3 become zero in elimination. If the right hand sude of your system is <b1,b2,b3> (Imagine this is a column vector) then how many solutions does your system...

Homework Statement Given the following matrix: I need to determine the conditions for b1, b2, and b3 to make the system consistent. In addition, I need to check if the system is consistent when: a) b1 = 1, b2 = 1, b3 = 3 b) b1 = 1, b2 = 0., b3 = -1 c) b1 = 1, b2 = 2, b3 = 3 Homework...

Homework Statement An infinitely long cylindrical capacitor with inner radius a and outer radius b carries a free charge per unit length of ##\lambda_{free}##. The region between the plates is filled with a nonmagnetic dielectric of conductivity ##\sigma##. Show that at every point inside the...

I understand for linear momentum the measure of the dificulty to take a body to the rest. But when I do the next exercises, I find that it requires less force for one body compared to the other with same linear momentum. Can someone explain me what to understand in an intuitive way what to...

The "Operator Norm" for Linear Transformations ... Browder, Lemma 8.4, Section 8.1, Ch. 8 ... ... I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra...

The "Operator Norm" for Linear Transfomations ... Browder, page 179, Section 8.1, Ch. 8 ... ... I am reader Andrew Browder's book: "Mathematical Analysis: An Introduction" ... ... I am currently reading Chapter 8: Differentiable Maps and am specifically focused on Section 8.1 Linear Algebra...

I was given the problem attached in the photo below and the first question is to define the decision variables and formulate the problem as a linear program. There are no solutions online, so it would be helpful if someone on the mighty PF could check them to see if they are correct, thanks...

Hi all. I am not a mechanical engineer but I've been working on an idea which consists of a linear shaft with Reciprocating motion. Since the device only works with rather a high speed shaft, I wanted to know what are the speed restrictions of a linear shaft? So let's give it some numbers. The...

What is the difference between tangential and linear acceleration of a circular object (let's say a ball)? Also, how does the torque contribute to linear acceleration?

Hi, The goal here is to increase/decrease the angle x by 5 degrees. the black circles represent a rubber tire (same as car tires, only smaller), 5cm in diameter, rotating on it's center, powered by a motor. each wheel has 40 psi (2.76 bar) of air in it. the yellow tray on both diagrams are...

So, my pre-algebra class is learning about linear relationships, but can anyone help explain it to me a little more? I tried google, but honestly, I want to hear other people before jumping to conclusions. So, my question is, what is a linear relationship?

The pioneering work by G. Lehmann, M. Taut, please see the attached files or download from wiley On the Numerical Calculation of the Density of States and Related Properties, http://onlinelibrary.wiley.com/doi/10.1002/pssb.2220540211/abstract The question is how the middle line of Eq. (3.9)...

Homework Statement Given the equations a) find the solution to the problem (1) in vectorial form, by first writing equation (1) in component form and then solving the two parts separately. These can then be combined to obtain the vector form of the solution. b) solve the results of the...

<Moved from a homework forum. Template removed.> I can't find any documentation on how to do this. I remember in linear algebra how to find the incidence matrix of an electrical network of purely resistors. Put how do I find it of a RLC circuit with resistors, inductors, and capacitors? I can't...

- This is the situation provided where it has to be demonstrated that linear momentum is not conserved or unrealistic. My assumptions are: there's no friction due to how Godzilla is moving, the sand is acting as a lubricant. Velocity is constant. This is an elastic collision. I also guess that...

Specifically, an elemental shear operation. I can prove how any existing linear dependency that exists persists with the new sheared vector, but I can't seem to prove that this shear operation does not introduce a linear dependency. I can see how the vector space between the 2 rows involved...

Hi PF! I am looping through a linear system and each time I do I generate a new matrix, call this matrix ##A##. When finding the eigenvalues of ##A## in Matlab is use [a,sigma2M] = eig(A);% a eigenvector and sigma2M matrix of eigenvalues sigma2(:,ii) = sum(sigma2M);% create matrix with rows of...

Homework Statement 2. Homework Equations 3. The Attempt at a Solution [/B]- So with the (from what i interpret of the notes this is needed) the same boundary conditions when time is fixed, we can relate the 'fundamental problem'- the initial condition ##t=0## given by a delta...

Homework Statement Verify that A^2-2A+7I=0Homework Equations A is a squared matrix and I is the identity matrix. The Attempt at a Solution I squared a matrix, which I called A, by multiplying the two A matrices together, then I subtracting the new matrix with the third matrix 2A, then I added...

Homework Statement Are ALL parallel plate capacitors linear? Homework Equations D = permittivity * E The Attempt at a Solution Capacitance is linear if permittivity is constant. Is there a case where a parallel plate capacitor is not linear?

Say you have a log-level regression as follows: $$\log Y = \beta_0 + \beta_1 X_1 + \beta_1 X_2 + \ldots + \beta_n X_n$$ We're trying come up with a meaningful interpretation for changes Y due to a change in some Xk. If we take the partial derivative with respect to Xk. we end up with...

I know there can be an infinite number of solutions when the objective function with 2 variables has an equal slope as a constraint's slope (assuming the constraint is affecting the feasible region and not a redundant constraint). How can you know there are multiple optimal solutions for...

Mod note: Member warned that the homework template is NOT optional find yp (particular integral) (D2 + 4D + 5) y = 2 e-2xcos(x) ((D+2)(D+2)+1) y = 2 e-2xcos(x) yp = [1/((D+2)2 + 1)] ⋅ 2e-2xcos(x) yp = e(-3)x ∫ ∫...

Homework Statement Design, giving the necessary ratings and characteristics necessary for the transformer, bridge rectifier, reservoir capacitor and regulator, a 12 V, 2 A regulated power supply. Also identify any heat sink requirements. The available mains supply is 230 V ±10% @ 50 Hz...

I am working with multiple regression with two independent variables, and interaction between them. the expression is: y = b1x1 + b2x2 and b3x1x2 The question is: does one center both independent variables at the same time, when checking for the significance of the effect of the independent...