Linear Definition and 1000 Threads

> 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...

a small business makes laptops and notepads. In any given month labour costs must not exceed £1350 and material costs must be a maximum of £1150. Relevant information: Laptops cost £50 in materials to make and labour costs £50, they make £110 profit on each laptop. notepads cost £25 in...

I'll try to be concise. I've been out of math for years and never truly learned to understand it. Until now. I want to put the growth mindset theory to the test and see if I can handle physics (or any STEM field) on a university difficulty. To verify if I'm up to it and even have the slightest...

Can someone explain the difference using concrete examples. I will attempt to explain my current understanding by example; A H atom has different energy levels which can be exactly described by algebraic functions with quantum numbers n, l etc. An electron can be excited from say the ground...

I. Free Fall Motion A mass m = 544 g is thrown straight up with an initial speed of 3.50 m/s from a height of h = 2.50 m Neglecting a drag force, determine: 1. The acceleration of the object while it moves up. 2. The acceleration of the object at the highest point. 3. The maximum height...

Homework Statement A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s, how high will the block rise after the bullet becomes embedded in it? Homework Equations 1. m1v1 +m2v2 = mfvf 2. x=xo +vot...

I am self teaching the subject but I am unsure of what is the whole point and picture

Homework Statement Solution of the differential equation ##(\cos x )dy = y (\sin x - y) dx , 0 < x < \dfrac{\pi}{2} ## is Homework EquationsThe Attempt at a Solution Only separation of variables, homogenous and linear DEs are in the syllabus, therefore it must be one of those. It obviously...

Homework Statement Linear Programming Case Study - Case Problem ( Page # 109 Decision making methods) “The Possibility” Restaurant? In the case problem, Angela and Zooey wanted to develop a linear programming model to help determine the number of beef and fish meals they should prepare each...

Homework Statement Let A:\mathbb R_2[x]\rightarrow \mathbb R_2[x] is a linear transformation defined as (A(p))(x)=p'(x+1) where \mathbb R_2[x] is the space of polynomials of the second order. Find all a,b,c\in\mathbb R such that the matrix \begin{bmatrix} a & 1 & 0 \\ b & 0 & 1 \\ c & 0...

I have been trying to prove the following theorem, for a finite dimensional vector space ## X ## and its dual ## X^* ##: Let ## f:X\rightarrow X^* ## be given by ## f(x) = (x|\cdot) ##, where ## (x|\cdot) ## is linear in the first argument and conjugate linear in the second (so I am using the...

any particular solution plus the general solution to the homogeneous equation. I'm having difficuilty understanding this proof from my lecture notes Theorem : Let T : V → W be a linear transformation. Let w ∈ W and suppose T(u0) = w T(v) = 0. where v ∈ V (the kernel ) to prove: T(u) = w...

Just a conceptual question : During a collision of two objects say A and B with the same mass, is the object with a higher velocity before collision never has its velocity increased after the collision, while the object with a lower initial velocity never has its velocity further decreased...

Homework Statement Given an nxn matrix, if a b exists so Ax=b has no solutions, can A be one-to-one? Homework Equations I understand that as a linear transformation, you need things such as (to be one-to-one as a linear trans) 1. n pivots 2. Only the trivial solution exists to Ax=0 Ax=b...

Hey, I need help with part D2. My explanation is not right so I honestly do not know what I am suppose to write. My assignment is attached to this thread.

Hi all, I have problem with regard to ill-conditioned linear system of solving sets of simultaneous equations using Mathematica program. I have tried my best to find a way to solve this but none was successful. I got results from m =1 and n =1 until m = 7 and n = 7, i,e. the systems are...

Homework Statement Find the equation of all planes containing the points P(2, -1, 1) and Q(1, 0, 0) Homework EquationsThe Attempt at a Solution I use PQ to get a vector, (-1, -1, 1). I some how need to use another vector so I can use the cross product to find the planes. So i let another...

I have a structure that needs to be pushed by a set of actuators. It is because 1 actuator's loading may not be sufficient and changing it to a more powerful model will just sacrifice my space which is not favorable. Can anyone tell me if it is a common way of doing it? If so, how do I manage...

Let W be a vector space and let A be a linear operator W --> W. Isn't it the case that for any such A, the kernel of A is the zero vector and the range is all of W? And that it is one-to-one from linearity? I ask because an author I am reading goes through a lot of steps to show that a certain...

Okay, so I'm down to the last equation. -12/11 x 10 + 54/11 I get -66/-99. Is this right? If so how do I put it into the graph. -12/11 x 10 = -120/110 + 54/11 = -66/99 (I think I've went wrong somewhere)

In linear accelerators that use a disk loaded structure (traveling wave), how would you calculate the iris(disk hole) radius, cavity radius, and disk thickness according to the wavelength

Hi! I'm need some help with this question: Decide $h$ so that the linear system $Ax=b$ has infinite solutions. $$A=\pmatrix{ 5 & 6 & 7 \cr -7 & -4 & 1 \cr -4 & 4 & 16 \cr}$$ $$b=\pmatrix{ 6 \cr 30 \cr h \cr}$$ I solved a similar question before but with A being a 2x2 matrix (and B a 2x1) and...

Homework Statement Homework EquationsThe Attempt at a Solution No clue really. I went ahead and tried to simplify this by turnining it into an echelon matrix. But I am sort of stuck now, since I can't divide by -k because I don't know whether or not it is equal to 0?

Homework Statement Solve the linear system of equations: ax+by+z=1 x+aby+z=b x+by+az=1 for a,b\in\mathbb R and plot equations and solutions in cases where the system is consistent. Homework Equations -Cramer's rule -Kronecker-Capelli's theorem The Attempt at a Solution Using Cramer's rule, we...

Homework Statement Plot the solution set of linear equations x-y+2z-t=1 2x-3y-z+t=-1 x+7z=8 and check if the set is a vector space. 2. The attempt at a solution Augmented matrix of the system: \begin{bmatrix} 1 & -1 & 2 & -1 & 1 \\ 2 & -3 & -1 & 1 & -1 \\ 1 & 0 & 7 & 0 & 8 \\...