Linear Definition and 1000 Threads

HI .I'm trying to prove that, for a linear transformation, it is worth that: f(a\bar{x}+b\bar{y})=af(\bar{x})+bf(\bar{y}) for every real numbers a and b. Until now, I have proved by myself that f(\bar{x}+\bar{y})=f(\bar{x})+f(\bar{y}). and , using this result i proved that: f(a\bar{v}) =...

Homework Statement Homework EquationsThe Attempt at a Solution I understand the solution of the problem, but I want to know why don't my approach work. I didn't change the frame of reference. I use the regular method of solving a torque problem. (mgsinθ - mAcosθ)(L/2) = mL2/3 θ'' which is...

Hy folks, Upfront I want to apologize for my writing and my dissability to use correct symbols to ease readability of the example. Ok now that that's done I just want to start upfront. If we set a usual example of an object falling from a tower with a height of x meters and assume that the...

Given an ##N## dimensional binary vector ##\mathbf{v}## whose conversion to decimal is equal to ##j##, is there a way to linearly map the vector ##\mathbf{v}## to an ##{2^N}## dimensional binary vector ##\mathbf{e}## whose ##(j+1)##-th element is equal to ##1## (assuming the index starts...

hello everyone,I want to construct the elliptical polarization in Jones's Matrix form . So, I use the linear polarizer to analyze this polarization. where the Intensity ,which obtain by using the linear polarizer,come from? by integrating overall angle or the other way ?

Below is a part proposed to be manufactured. The inspection of this part poses a problem, because vernier callipers only measure distances between parallel surfaces. I know there is some photographic method of measuring distances, however I would like to know is there no way of physically...

I have a picture below please have a look at it. The guy is using two conducting rods placed parallel to each other and placed below it are magnets. When battey is connected to rods and a conductor is placed over them it starts to move.That works according to flemmings left hand rule. I was...

Why is y = mx + b called the slope-intercept form? Why is m the chosen variable for slope? Why is b the chosen variable representing the y-intercept?

How do i solve d= Lh/R1+R2. How do i also solve d= LM/R2+R1.

I have a data set of 11 predictors and one response for 1000 observation and i want to do linear regression. I also have measurements errors of the predictors (also 11X1000 matrix) and i need to count for them in the total error estimation. how can i do that?

<Moderator's note: Continued from a technical forum and thus no template. Re-opening has been approved by moderator.> Hi, my question is related to simplex algorithm anticycling rule called Bland's rule. While I was working with the proof in the link...

Assume that the Earth is a sphere with a radius of 3,960 miles and a rotation of 1 revolution per 24 hours. A. Find the angular speed. Express your answer in units of radians/sec, and round to two significant digits. B. Find the linear speed of a point on the equator. Express the answer in...

You are given the rate of rotation of a wheel as well as its radius. For A-C, determine the following: A. The angular speed, in units of radians/sec. B. The linear speed, in units of cm/sec, of a point on the circumference of the wheel. C. The linear speed, in cm/sec, of a point halfway...

I have learned that for matrix theory, for ##A \vec{x} = \vec{b}##, if there exists a particular solution ##p##, then every solution looks like ##p+k##, where ##k \in \ker A##. Can someone help me find material on this online, but only in the context of general linear transformations? For...

This is from Kreyszig's Introductory Functional Analysis Theorem 2.9-1. Let $X$ be an n-dimensional vector space and $E=\{e_1, \cdots, e_n \}$ a basis for $X$. Then $F = \{f_1, \cdots, f_n\}$ given by (6) is a basis for the algebraic dual $X^*$ of $X$, and $\text{dim}X^* = \text{dim}X=n$...

Hi I have a problem dealing with rpm power and torque. I have a motor powering a gearbox which has a 20:1 ratio. The power and rpm are not an issue so i have not looked at those figures but the motor produces 240Nm of torque. Since it is a 20:1 gearbox, i have assumed the torque is 20 times...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

Dear Everybody, I have a question about an example: "Solve the system: $x'(t)=3x(t)-4y(t)+1$ $y'(t)=4x(t)-7y(t)+10t$ We write the system using the operator notation: $(D-3)[x]+4y=1$ $-4x+(D+7)[y]=10t$ We can eliminate x from this system by adding 4 times the first equation to $(D-3)$...

Hello, Can someone please let me know of a resource (book or other) that explains how to use ANOVA in linear regression? I didn't even know what ANOVA was until some days ago so I'm looking for something that explains it thoroughly with deductions. The resources I've read focused solely on...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on $$\mathbb{R}^n$$" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows...

I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ... I am currently focused on Chapter 9: "Differentiation on ##\mathbb{R}^n##" I need some help with the proof of Proposition 9.2.3 ... Proposition 9.2.3 and the preceding relevant Definition 9.2.2 read as follows: In the...

Post moved by moderator, so missing the homework template. series ##{a_n}## is define by ##a_1=1 ## , ##a_2=5 ## , ##a_3=1 ##, ##a_{n+3}=a_{n+2}+4a_{n+1}-4a_n ## ( ##n \geq 1 ##). $$\begin{pmatrix}a_{n+3} \\ a_{n+2} \\ a_{n+1} \\ \end{pmatrix}=B\begin{pmatrix}a_{n+2} \\ a_{n+1} \\ a_{n} \\...

Homework Statement convert: Y − 200 = −4 (X − 15) to X = −0.25 ⋅ Y + 65. with a given Δy/Δx = -36/4 Homework Equations point slope, slope intercept The Attempt at a Solution I understand point slope, slope intercept, and standard form, I understand how to convert one to the other, but I...

Hello, I am a new member looking for the answer to a question I recently had on an exam. I will not know if I got it right for up to 6 weeks so am curious. Question is: A faucet drips water at 5 drops per second. calculate the distance in metres between the first and second drop after the first...

A problem that I have to solve for my Linear Algebra course is the following We are supposed to use Mathematica. What I have done is that I first checked that A is symmetric, i.e. that ##A = A^T##. Which is obvious. Next I computed the eigenvalues for A. The characteristic polynomial is...

I want to find solution to following ODE $$ \frac{d \bar h}{dt} + \frac{K}{S_s} \alpha^2 \bar h = -\frac{K}{S_s} \alpha H h_b(t) $$ I have solved it with integrating factor method with ## I=\exp^{\int \frac{1}{D} \alpha^2 dt} ## as integrating factor and ##\frac{K}{S_s} = \frac{1}{D} ## I have...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of Example 2.2.5 ... ... Duistermaat and Kolk's Example 2.2.5 read as follows: In the above text by D&K we...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 2: Differentiation ... ... I need help with an aspect of Example 2.2.5 ... ... Duistermaat and Kolk's Example 2.2.5 read as follows: In the above text by D&K we...

Hello. My problem is that I began with Linear Approximation and I'm terribly stuck. I have problems understanding its very concept and with calculations. (It may sound stupid but I'm autodidact and I'm studying mathematics in english (not my mother tongue) and sometimes it gets hard). It would...

Homework Statement How to obtain the "1" highlighted? Homework Equations multiply by μ then by dt (integration )to both sides The Attempt at a Solution [/B] lets just consider part "2y/t": ∫2y/t from pi/2 to t =ln(t^2/(pi^2/4)) from pi/2 to t =ln1-ln(t^2/(pi^2/4)) = -ln(t^2/(pi^2/4)) how...

Hey, I have a problem where I have a discrete independent variable (integers spanning 1 through 27) and a continuous dependent variable (50 data points for each independent variable). I am wondering about the best method of regression here. Should I just fit to the mean or median? Is there a way...

Is linear attenuation coefficient a constant for a given material or will it depend on the thickness of the material?

Homework Statement Given random vector ##X'=[X_1,X_2,X_3,X_4]## with mean vector ##\mu '_X=[4,3,2,1]## and covariance matrix $$\Sigma_X=\begin{bmatrix} 3&0&2&2\\ 0&1&1&0\\ 2&1&9&-2\\ 2&0&-2&4 \end{bmatrix}.$$ Partition ##X## as $$X=\begin{bmatrix} X_1\\X_2\\\hline X_3\\X_4\end{bmatrix}...

I am reading "Multidimensional Real Analysis I: Differentiation" by J. J. Duistermaat and J. A. C. Kolk ... I am focused on Chapter 1: Continuity ... ... I need help with an aspect of Example 1.8.14 ... ... The start of Duistermaat and Kolk's Example 1.8.14 reads as...

Homework Statement For what value(s) of k is the linear system with augmented matrix inconsistent? Homework Equations None. The Attempt at a Solution I know that inconsistent means no solution. So do I set k=2k and solve for k?

Hey! :o We want to construct a linear spline that at the points $x_0=-1$, $x_1=0$, $x_2=1$ has the values $b_0=0$, $b_1=1$ and $b_2=3$. The spline should get from $S_{x,1}$ with $x=\{x_0, x_1, x_2\}$ to $[-1,1]$. Do we want to find a function of the following form...

Homework Statement Let A be an arbitrary m× n matrix. Find a matrix C such that CA = B for each of the following matrices B. a. B is the matrix that results from multiplying row i of A by a nonzero number c. b. B is the matrix that results from swapping rows i and j of A. c. B is the matrix...

Homework Statement The initial speed of a ball up an inclined plane is 3 m/s upwards. The ball reaches its highest point after 1.2 seconds. a) find the acceleration. b) how far has the ball gotten during this time? c) how far has the ball rolled after 0.4 s and after 2.4 seconds? Homework...

Homework Statement [/B] Suppose the solution set of some system Ax = b , Where A is a 4x3 matrix, is *Bold characters are vectors* x_1= 1 + 3t x_2 = 2 - t x_3 = 3 + 2t where t is a parameter and can be any number. a) How many pivots are in the row echelon form of A? b) Let u, v, w be the...

Homework Statement A 10 g bullet traveling at 400 m/s strikes a 10 kg , 1.2-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door immediately after impact? Homework Equations p[/B]= mv L = Iω...

hi, my question is related to a proof involves bland rule for avoiding the degeneracy. Initially I emphasized some sentences which have importance in attachment/file with yellow color. At the beginning, it says xs is entering variable and when it enters objective value does not change( because...

I have not really finished studying linear algebra, I have to admit. The furthest I have gotten to is manipulating matrices a little bit (although I have used this in differential equations to calculate a Wronskian to see if two equations are linear independent, but again, a determinant is...

Homework Statement This is for a linear algebra class, but it's taught my mathematicians, for mathematicians and not physicists or engineers so we write pseudo-proofs to explain things. In Exercises 37–40, let T be the linear transformation whose standard matrix is given. In Exercises 37 and...

Hello, I am having a bit of trouble understanding the concept of Rayleigh scattering as it relates to light from the sun. My book states that unpolarized light will hit the atmosphere, and the scattered light will be mainly horizontally polarized, while the unscattered light remains...

This question is regarding equation 6.59 in Classical Mechanics Goldstein 3rd edition. I don't understand how he reaches that step. He says he does by inverting 6.41. Is he taking the transpose matrix composed of the eigen vectors by meaning inversion ? I thought I could upload the screenshot...

Hello, I measured an object using an electric scale. It is 5kg. I want to select a linear actuator such that when placed vertically, it can keep the object on hold at a fixed height. In this case, what static load (in lbs and Netwon) should the actuator be capable of handling? I am confused by...

I am to try to find simple way to spin a spinning flywheel. What linear motion device acting on the outside edge of a spinning flywheel can be used to increase the speed of the flywheel. Need to use a repeating pattern such as pushing your hand down over and over on the edge of the wheel to...

Hi, I have in a previous thread discussed the case where: \begin{equation} TT' = T'T \end{equation} and someone, said that this was a case of non-linear operators. Evidently, they commute, so their commutator is zero and therefore they can be measured at the same time. What makes them however...