Linear Definition and 1000 Threads

The average weight of a male child’s brain is 970 grams at age 1 and 1270 grams at age 3. (Source: American Neurological Association) Assuming that the relationship between brain weight y and age t is linear, write a linear model for the data. I am going to start by saying y = mx + b. Let x...

A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use. Let t =...

A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of 7% of sales. Write a linear equation for the salesperson’s monthly wage W in terms of monthly sales S. I will let W(S) = monthly wage W in terms of monthly sales S. $5000 plus a commission of 7% of sales =...

Hello! If I have some data points, with error bars on both x and y, and I would like to fit them with a function f(x). How can I write the chi-squared in this case? For errors only on y, I would have ##\chi^2 = \sum_i(\frac{f(x)-y}{\sigma_y})^2##, but I am not sure how to include ##\sigma_x##...

Hi, In simple regression for machine learning , a model : Y=mx +b , Is said AFAIK, to have bias equal to b. Is there a relation between the use of bias here and the use of bias in terms of estimators for population parameters, i.e., the bias of an estimator P^ for a population parameter P is...

Hello: I'm not sure if there's an accepted canonical form for a quadratic equation in two (or more) variables: $$ax^2+by^2+cxy+dx+ey+f=0$$ Is it the following form? (using the orthogonal matrix Q that diagonalizes the quadratic part): $$ w^TDw+[d \ \ e]w+f=0$$ $$w^TDw+Lw+f=0$$ where $$...

Summary:: Linearizing an equation for MILP Hi All I have Linear programming problem where I need to linearise the following function: Y = A * log2(1 + (Bx/Cx^2)). where A, B and C are constants. Can you please help or advise?

Hi, as follow-up to this thread I've a question about general representation of a two-port network. Basically it is ad hoc built four-terminal linear network (using controlled sources + nullator-norator pair): for it I found a general representation ##AV + BI = 0## as in the picture above. If...

I have a pencil of Iron of length ##L## rotating about its center in a plane at constant angular velocity ##\omega##. The tip of the pencil in Newtonian mechanics has linear velocity ##\frac{\omega L}{2}##. It can exceed ##c##, of course. Now let us complicate this. Assume the center of the...

Homework Statement:: Hi, I'm looking for an exercise involving a linear motor, but on my physics book there are none Relevant Equations:: Lenz Law, Maxwell's equation Hi, everyone I'm looking for an exercise involving a linear motor, but on my physics book there are none. Do you happen to...

I solved it by two methods: ----------------------------------------------------- First, by conservation of linear momentum, using the vector velocities of each particle: In the imminence of the impact, the velocity of all the three particles are the same, \vec v_0 = - \sqrt{2gh} \hat j...

The linear combination of the eigenfunctions gives solution to the Schrodinger equation. For a system with time independent Hamiltonian the Schrodinger Equation reduces to the Time independent Schrodinger equation(TISE), so this linear combination should be a solution of the TISE. It is not...

Can I create a nonlinear spring, for a nonlinear oscillator, by putting many linear springs in series and parallel?

Hello! I need to check if this transformation (not sure if it is the right word in English) from ## R^3 to R^3 ## is linear f(x1,x2,x3) = f(sin(x1),x2+x3,0). Now we are given that the transformation is linear if this you can prove this statement. $$f(\lambda * u + \mu * v) = \lambda * f(u) +...

What are the suitable books in linear algebra for third course for self-study after reading Linear Algebra done right by Axler and Algebra by Artin?

Each operator has a domain, so for a power of an operator to exist, the domain of the operator must remain invariant under the operation. Is that correct? mentor note: edited for future clarity

y=mx+c by z=log y axis m=9-2.5 / 35 = 13/70 z=13/70 * (t-1983) + 2.5 log y = 13/70 * (t-1983) + 2.5 # doubling time: t1=y1, t2=y2=2y1 log y1 = 13/70 * (t1-1983) + 2.5 ---{1} log (2*y1) = 13/70 * (t2-1983) + 2.5 ---{2} {2}-{1}: log2=13/70 * [(t2)-(t1)] [(t2)-(t1)] = log2/(13/70) # for log...

My guess is that since there are no rows in a form of [0000b], the system is consistent (the system has a solution). As the first column is all 0s, x1 would be a free variable. Because the system with free variable have infinite solution, the solution is not unique. In this way, the matrix is...

Hi MHB! I recently came across a problem and I was thinking most likely I was missing something very obvious because I couldn't make sense of what was being asked, and I so wish to know what exactly that I failed to relate. Question: Find the minimum of $6\sin x+8\cos x+5$. Hence, find the...

Would you call it an inverse relationship or a linear relationship, what is the correct terminology?

What are best second course(undergraduate) books in linear algebra for self-study?I have already read Introduction to Linear Algebra by Lang.

We know that impulse is $$\vec J = \vec F \Delta t = \Delta \vec p$$ Let ##l, m## be the length of single rod and its mass respectively. Analyzing torques and forces on each rod separately we have: Rod ##AC##: $$F\Delta t +N_x\Delta t = mV_{ac,x} \space\space\text{ eq. }(1)$$ $$F\Delta t\cdot...

Hi, I was working on the following homework problem and just wanted to check whether my thoughts were along the right lines: "Explain briefly why a linear filter would not be appropriate for removing impulsive noise in a signal, and suggest an alternative filter." Attempt: When we use a linear...

Hey all. This is about Ohm's Law (and specifically resistance). When you plot the change in current vs the change in voltage you should get a linear trend line (providing it is from an ohmic device). The gradient should be the resistance. My questions is why does the gradient value need to be...

I have the following equation to solve for the coefficients b: \sum\limits_{m,n=0}^N b_m b_n^* (x_{mn}+y_{mn}) e^{ ik (ux_{mn} + vy_{mn}) } = 0 which must be satisfied for all u and v in the interval [-1,1]. Here k is a constant, b is a vector of length N with unit norm ||b||^2=1, and x and y...

Many circuit analysis techniques only apply to linear circuits. I don’t quite understand how to distinguish between linear and non-linear circuits. I understand the mathematical concept of linearity. I understand why components like resistors, capacitors and inductors are linear. I don’t quite...

Hello, With multivariate linear regression, there is a single dependent variable ##y## and multiple independent variables ##x_1##, ##x_2##, ##x_3##, etc. There is a linear, weighted relationship between ##y## and the various ##x## variables: $$ y = c_1 x_1 + c_2 x_2 + c_3 x_3 $$ The...

ok we are supposed to go to here Find 3 different matrices that reflect the following transformations, report the matrix, the determinant, and the eigenvalues. 1. Rotation by $\dfrac{\pi}{4}$ 2. Shear along $x$ by a factor of $k$ 3. Reflection by the line $\theta$ there are some more but the...

if $Q(\theta)$ is $\left[\begin{array}{rr} \cos{\theta}&- \sin{\theta}\\ \sin{\theta}&\cos{\theta} \end{array}\right]$ how is $Q(\theta)$ is a linear transformation from R^2 to itself. ok I really didn't know a proper answer to this question but presume we would need to look at the unit...

Hi, I was trying to do the following problem. My attempt. Finding the reduced row echelon form for the system above. I do not see any way to proceed any further. The following is the solution presented in solution manual. How do I proceed to get the following answer?

So the reason why I'm struggling with both of the problems is because I find vector spaces and subspaces hard to understand. I have read a lot, but I'm still confussed about these tasks. 1. So for problem 1, I can first tell you what I know about subspaces. I understand that a subspace is a...

I want to use the point reactor kinetics equations to solve for the power as a function time when a reactivity of gamma*t is added to a reactor that is at equilibrium at time 0. I am also asked to consider the case where the transients are long-lived compared to the lifetime of prompt neutrons...

Hello, I am working on a mechanics project, on which I encounter a problem that I am sure others have faced before. I have tried to find answers here and there by typing keywords, but I can't find what I am looking for. Here is the context: Two horizontal plates are separated by a...

So if I am understanding the question correctly, I need to find the change in temperature that causes one rights outer radii to be the same as another rings inner radii. Now what I tried is two equations change length_1= a_1*original length_inner * change in temp change length_2= a_2*original...

To find the mass in other pan, i need to find the force caused by beads on the pan ∴ KEinitial + PEinitial = KEfinal + PEfinal 0 + mgh = ½ mv^2 => v = 3.13 m/s ∴ The change in momentum : p2 - p1 = m ( v2-v1) = m( v - (-v)) = 2mv ∴ F = Δp / Δt = n. m. v How can i apply the rate of 100...

$ v=\left[\begin{array}{r} -3\\-4\\-5\\4\\-1 \end{array}\right] w=\left[\begin{array}{r} -2\\0 \\1 \\4 \\-1 \end{array}\right] x=\left[\begin{array}{r} 2\\3 \\4 \\-5 \\0 \end{array}\right] y=\left[\begin{array}{r} -2\\1 \\0 \\-2 \\7 \end{array}\right] z=\left[\begin{array}{r} -1\\0 \\2 \\-3...

Hey! :giggle: Question 1 : Let $g(x)-=x-x^3$. The point $x=0$ is a fixed point for $g$. Show that if $x^{\star}$ is a fixed point of $g$, $g(x^{\star})=x^{\star}$, then $x^{\star}=0$. If $(x_k)$ the sequence $x_{k+1}=g(x_k)$, $k=0,1,2,\ldots$ show that if $0>x_0>-1$ then $(x_k)$ is...

Hello, thanks in advance, I do many many things, jack of all trades but master of none. Would some one be willing to help me with some formulas and calcs for making my own linear solenoid? I can give the final specs I'm after then I could use advice on materials and other variables. I'd like...

I tried hard to understand what this author proposed, but I feel like I failed miserably. My attempt of solution is here: Item (a) is verified in the case where ##n = 2##, since ##F## being a linear transformation, by the Corollary of the Nucleus and Image Theorem, ##F## takes a basis of...

This is my c program below. Again everything works as expected up until the highlighted lines or the second for loop. When i run my program to output the arrays contents i get bizarre numbers that are not correct. # include <math.h> # include <stdlib.h> # include <stdio.h> # include <time.h>int...

Hey! :giggle: Question 1: Let $C$ be a $\mathbb{R}$-vector space, $1\leq n\in \mathbb{N}$ and let $\phi_1, \ldots , \phi_n:V\rightarrow V$ be linear maps. I have shown by induction that $\phi_1\circ \ldots \circ \phi_n$ is then also a linear map. I want to show now by induction that if $V$ is...

hi guys i was trying to use this shooting algorithm from Xue and Chen Scientific Computing with MATLAB book : to solve this non linear temperature distribution problem : i checked my Matlab function multiple times but i am keep getting a nonsense graph for the temperature , can someone cheak...

PROGRAM DensityOfState IMPLICIT NONE INTEGER :: omega , t0 , a0 ,kx omega=1 ; t0 =1 ; a0=1 REAL :: kx , eta , w , ek eta=0.0015 REAL,PARAMETER :: pi=3.14 COMPLEX , PARAMETER ::i=(0,1) COMPLEX :: Energy COMPLEX :: Density COMPLEX :: GreenFunc...

the matrix at the bottom is from eMH but thot this was the way to do it... maybe not!

Textbook answer: "If P1P2 = P2P1 then S is contained in T or T is contained in S." My query: If P1 = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{pmatrix}and P2 =\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \\ \end{pmatrix} as far as I...

$\tiny{311.1.1.26}$ Construct 3 augmented matrices for linear systems whose solution set is $x_1=3, \quad x_2=-2, \quad x_3=-1$ ok the only thing I could think of is just rearrange the rows of an RREF matrix. albeit losing the triangle format hopefully no typos $\left[\begin{array}{rrr|rr} 1&...

Here I'm going to show all that I've understood - 1. 2. 3. What I've attempted - L = Lo (1+ α * ẟT) ẟT = 150°C - 15°C = 135°C (Steel) L = ẟL (1 + 11 * 10^-6 * 135) (Copper) L = ẟL (1 + 17 * 10^-6 * 135) This doesn't get me anywhere, obviously. Am I supposed to understand from the...

%%% Assume that ##X/Y## is defined. Since ##\dim Y = \dim X##, it follows that ##\dim {X/Y}=0## and that ##X/Y=\{0\}##. Suppose that ##Y## is a proper subspace of ##X##. Then there is an ##x\in X## such that ##x\notin Y##. Let us consider the equivalence class: ##\{x\}_Y=\{x_0\in...

I have to study the solutions of the following system of three equations and three unknowns upon variation of parameters k and h. ix1+kx2-x3 = 1+i (k+i)x1+(1-i)x2-(ik-1)x3 = h kx1+(4+2i)x2-(k-3-3i)x3 = 1-i Obviously i is the imaginary unit. And as stated k and h are the parameters . I can't...