Linear Definition and 1000 Threads

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...

'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?

Homework Statement For the linear transformation T: R2-->R2 defined by T(x1, X2) = (x1 + x2, 2x1 - x2), use the matrix A to find T(v), where v = (2, 1). B = {(1, 2), (-1, 1)} and B' = {(1, 0), (0, 1)}.Homework Equations T(v) is given, (x1+x2, 2x1-x2) The Attempt at a Solution Okay, I see...

Hello everyone, I am not an engineer, so I apologize if this is a relatively simple question. What's the best way to turn rotational motion into linear motion under the following circumstances? 1. Rotational motion is driven by a vertical bolt. 2. When turned, the bolt will extend a bar...

Hello, i have been studying for finals and i am stuck on a question on my study guide. the question is to make a scatter plot of a set of data, find the equation of the best fit line, and approximate the value of y for x = 5. the data is like this: x: 0 2 4 6 7 and the y is like : y: 2 7 14...

Homework Statement Consider the vector space R2 with the standard inner product given by ⟨(a, b), (c, d)⟩ = ac + bd. (This is just the dot product.) PLEASE SEE THE ATTACHED PHOTO FOR DETAIlS Homework Equations T(v)=AT*v The Attempt at a Solution I was able to prove part a. I let v=(v1,v2)...

Homework Statement Prove the following: Let V be a vector space and assume there is an integer n such that if (v1, . . . , vk) is a linearly independent sequence from V then k ≤ n. Prove is (v1, . . . , vk) is a maximal linearly independent sequence from V then (v1, . . . , vk) spans V and is...

Homework Statement Prove the following theorem: Let (v1, . . . , vk) be a sequence of vectors from a vector space V . Prove that the sequence if linearly dependent if and only if for some j, 1 ≤ j ≤ k, vj is a linear combination of (v1, . . . , vk) − (vj ). Homework EquationsThe Attempt at a...

Hi everyone. I am tackling a problem related to the purchase of items that are available from different vendors, and from what I've seen so far it seems to me that it may be solvable by linear programming methods (I'm using R). However I'm not sure how to set up the problem to achieve the exact...

Computer science major here. I recently completed calculus I, II, III. Now I know that I'll probably be required to take linear algebra. So far, I expect to do some Gaussian elimination (assuming I know what a row echelon is). What else should I expect from linear algebra?

I want to try to predict the USA summer highs using a linear regression. I know I can probably take data from the last 10 summers and plug that in, and use that to predict, but I'd like to use two data sources. 1 data source from the historical highs from past summers in the USA, and the 2nd...

If you have: A Linear Induction Coilgun, basically like a series of Induction Furnaces, using copper coils with high AC current at a high frequency. Where the projectile traveling inside those coils has a shorted superconducting coil around the outside of it, embedded in the ceramic projectile...

I'm having trouble getting started on this one and I'd really appreciate some hints. This question comes from Macdonald's Linear and Geometric Algebra book that I'm using for self study, problem 2.2.4. Homework Statement Let U1 and U2 be subspaces of a vector space V. Let U be the set of all...

Homework Statement The optical power of a HeNe -laser is ##P_0 = 5.0mW## and the wavelength ##\lambda = 633nm##. The emitted light is linearly polarized. As the laser beam travels through two in-series -polarizers, the power detected behind the second polarizer ##P_2 = 1mW## . If the first...

Homework Statement Two cars collide head on but offset from each others center of gravity. After the impact the two cars are locked together as one body. Due to the location of the collision point, the impact causes the two locked cars to spin clockwise. Car A- traveling west going 10 mph...

Linear actuator spec.: 400mm stroke, 6000N, 2 limit switches, 5mm/sec, 12V DC supply, BIBUS IP65 casing. One of the limit switches of my LA (Linear Actuator) seems to have burned out. This happened because I accidentally plugged the LA leads into the AC mains socket (my LA is rated to run at...

Homework Statement i am doing homework about linear equations, i am just asking if i am ok, whith my selection the question is: from the next equations, which ones are line equations, in x1,x2 and x3? Homework Equations [/B]The Attempt at a Solution the next are line; a,c,f the next arent...

Homework Statement Find the SVD of Homework EquationsThe Attempt at a Solution I'm stuck My question is why in the solution it originally finds u_2=[1/5,-2/5]' but then says u_2=[1/sqrt(5),-2/sqrt(5)]'. I don't see what math was done in the solution to change the denominator from 5...

This is where I am stuck. I studied ordered basis and coordinates vector previous to this. of course I studied vector space, basis, linear... etc too, However I can't understand just this part. (maybe this whole part) Especially this one which says [[T(b1)]]c...[[T(bn)]]c be a columns of...

Given a linear homogeneous 2nd order ODE of the form $$y''(x)+p(x)y'(x)+q(x)=0$$ the general solution is of the form $$y(x)=c_{1}y_{1}(x)+c_{2}y_{1}(x)$$ where ##c_{1},c_{2}## are arbitrary constants and ##y_{1}(x), y_{2}(x)## are linearly independent basis solutions. How does one prove that...

micromass submitted a new PF Insights post How to Self-study Algebra: Linear Algebra Continue reading the Original PF Insights Post.

Homework Statement [pardon my crude drawing] Say I have a ball that hits the a rod at rest pivoted around hinge A. The ball in the diagram is the solid black, and the rod is the thin line in the diagram and is rotating around the square-shaped hinge at the bottom. I am not an artist but...

Homework Statement Let T: P4--->P3 be a linear transformation given by T(p)=p'. What is the kernel of T? Homework EquationsThe Attempt at a Solution T(a0+a1+a2x2+a3x3+a4x4)=a1+2a2x+3a3x2+4a4x3 Ker(T)= { T(p)=0} so, a1+2a2x+3a3x2+4a4x3=0 then a1=2a2x+3a3x2+4a4x3 Ker(T)= { (-2,1,0,0)...

https://www.math.ucdavis.edu/~anne/linear_algebra/

I know the arrow -> means a map. For example, defines a linear map. But I cannot figure out what does a X mean? I know that above denote a inner product map. whatever is on the left of the : is defined by whatever is on the right. but what is the x symbol? What is the correct way to read...

Homework Statement Let A be an n×n matrix which has the property that A^2 =A. (i) Write down the most general polynomial in AHomework EquationsThe Attempt at a Solution My biggest problem is that I don't even understand what the question is asking Is it just sum (alphaA^n)=0 but A^n=A...