Linear Definition and 1000 Threads

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...

> Admit that $V$ is a linear space about $\mathbb{R}$ and that $U$ and $W$ are subspaces of $V$. Suppose that $S: U \rightarrow Y$ and $T: W \rightarrow Y$ are two linear transformations that satisfy the property: > $(\forall x \in U \cap W)$ $S(x)=T(x)$ > Define a linear transformation $F$...

Admit that V is a linear space about \mathbb{R} and that U and W are subspaces of V. Suppose that S: U \rightarrow Y and T: W \rightarrow Y are two linear transformations that satisfy the property: (\forall x \in U \cap W) S(x)=T(x) Define a linear transformation F: U+W \rightarrow Y that...

Homework Statement Let(v1, v2, v3) be three linearly independent vectors in a vector space V. Is the set {v1-v2, v2-v3, v3-v1} linearly dependent or independent? Homework Equations Linearly independent is when c1v1+c2v2+...+ckvk=0 and c1=c2=...ck=0 The Attempt at a Solution c1(v1-v2)+...

Homework Statement I'm told to find the matrix Q of the matrix A Homework EquationsThe Attempt at a Solution So my problem is that in the answer key they have S = (1/3)... and I have no idea where this 1/3 comes from. I get an equivalent answer for X_1, X_2, and X_3 S = [X_1, X_2, X_3] but...

which has higher failure rate: linear algebra or intro to programming. I understand failure rate might be skewed: math majors, who are gifted and interested in math, are required to take linear algebra but not intro to programming, while CS majors are required to take both. Which class do CS...

Given the non-zero vectors u, v and w in ℝ3 Show that there is a non-zero linear combination of u and v that is orthogonal to w. u and v must be linearly independant. I am not really sure at all. But I have done this: This is a screenshot of what I have done. Basicly, I assumed in the end...

Question: By what factor has the linear size-scale of the Universe changed between when the light was emitted from the galaxy and now? The question gives the red shift z and I have the equation linear size scale = 1 / 1 + z and I know how to calculate the linear size scale. But I'm a little...

Homework Statement Suppose y(t) is a complex-valued solution of y'' +py' + qy=0 where p and q are real numbers. Show that if y(t)=yre(t) + iyim(t), where yre(t) and yim(t) are real valued, then both yre(t) and yim(t) are solutions of the second-order equation. Homework Equations We can use the...

Fourier Transform of Piecewise linear spline wavelet is defined by 1-|t|, 0<t<1; 0, otherwise, is (sinc(w/2))^2. Can anyone please show me the steps. Thanks

Homework Statement A uniform, 4.5-kg, square, solid wooden gate 1.5 m on each side hangs vertically from a frictionless pivot at the center of its upper edge. A 1.1-kg raven flying horizontally at 5.0m/s flies into this door at its center and bounces back at 2.0m/s in the opposite direction...

Homework Statement a small 0.199 kg block slides down a frictionless surface through height h = 0.608 m and then sticks to a uniform vertical rod of mass M = 0.398 kg and length d = 2.23 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ. point O is at the end...

Homework Statement Let R2 have the Euclidean inner product and use the Gram-Schmidt process to transform the basis {u1,u2} into an orthonormal basis. u1 = (1,-3) u2 = (2,2) Homework Equations Gram-Schmidt process: \\v_1 = u_1 \\v_2= u_2 - \frac{\left ( \left \langle u_2, v_1\right \rangle...

Homework Statement I'm trying to solve this circuit when I try to simulate and run a dc sweep i get that it can't be solved. When I try to find the answer using linear algebra I get this answer after I throw it into MATLAB with the warning “[w]arning: Matrix is close to singular or...

Homework Statement I feel like I should know the answer to this, so I believe this to be an easy question. Say have matrix A, and I store the elimination matrices E_1,1 E_2,1 etc. and somewhere in the elimination process I have to use a permutation matrix to swap rows. My question is when I...

Homework Statement So I think I found an error in the solution were it attempts to find q_2^ I'm asked find the orthornomal basis for the column space of matrix A. Homework EquationsThe Attempt at a Solution [/B] My question is in what it puts for q_2^ A_2 = [4/3 4/3 -2/3]^T ||A_2|| =...

Homework Statement A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block, and as a result of the perfectly inelastic impact...

Hi, I'm building a toy and I'd like it to spin around a vertical shaft but also move freely up and down while it is rotating. Also, I'd like that the rotating body will get spinned using a gear which will be positioned in a fixed location on the shaft (at the bottom) while the rotating body...

Homework Statement Let L: ℝ2→ℝ2 such that L(x1, x2)T=(1, 2 ; 3, α)(x1, x2)T=Ax Determine at what values of α is L an isomorphism. Obviously L is given in matrix form. The Attempt at a Solution First of all a quick check, dim (ℝ2)=dim(ℝ2)=2 Ok. An isomorphism means linear transformation which...

1. Homework Statement The problem is shown in the photo above. I would like to discuss part B. Homework Equations conservation of linear momentum The Attempt at a Solutionthe solutions say that we should have the following approach: Mb*vb = [Mb + Ms] * vFinal. Plug in the numbers and get vF...

Homework Statement I feel like this is a easy question but it seems the answer key doesn't seem to be right. So say I have 2 vectors and I'm trying to find the projection of vector u perpendicular to the vector v Homework EquationsThe Attempt at a Solution So I don't remember doing...

Homework Statement I ask for help in solving the exercises in this project on applied linear algebra. The problem outlined in the project is one in which we are tasked with modeling the demise of a gambler. I need help solving exercise 1 (in red) on page 6. I have pasted the exercise text...

Homework Statement So yeah I'm doing a project were I get to create a problem. I would like to learn how to solve a AC RLC circuit using linear algebra. I'm trying to find all of the currents on the edges of the graphs and find all of the voltages at the nodes connecting the edges. I don't...

Homework Statement I did an experiment involving the speed of sound at different temperatures. I placed two microphones at a fixed distance apart and I measured the time taken for a sound wave to travel between the two mics. I repeated this for different temperatures. I want to make a graph for...

Homework Statement I got following Question from a book: I am doing it using a different method but my answer is wrong. Can somebody please guide me, what is the problem with it?? The question is:In 1999, Diana read 10 English books and 7 French books. In 2000, she read twice as many French...

Hi everyone, I have always been confused by momentum and linear inertia. What exactly is the difference between them? Aren't them both resistance to change in motion? Its hard to explain what I am confused with so here's an example: if there are 2 moving cars traveling at the same speed and car...

Homework Statement These questions are related to an experiment where we had to record the current for varying values of potential difference (10 readings), then repeat the process with the applied potential difference was reversed a) Why is the resistance of a light bulb not constant? b) Does...