Linear system Definition and 149 Threads

y(t) = x(t) + \int (t - \tau)x(\tau)d\tau for it to be linear, T[kx(t)] = kT[x(t)] so i have T[kx(t)] = kx(t) + \int (t - \tau)x(\tau)d\tau and kT[x(t)] = k[x(t) + \int (t - \tau)x(\tau)d\tau] = kx(t) + k\int (t - \tau)x(\tau)d\tau so they aren't equal and aren't linear. however, I'm not sure...

I am solving for a linear system of differential equations. Since LaTeX never works out for me on this forum, I have written out my problem and my solution on LaTeX and made an image of it: http://i.imgur.com/ncra.jpg . I basically have to solve the system of equations and express it as a...

Dear all: For a standard linear system, y(n*1)=A(n*n)x(n*1) If y is exact and A is well-conditioned, it is easy to calculate x. However, if y has some disturbances or some errors, at the same time, A matrix is ill-conditioned. It is difficult to accurately obtain vector x...

Homework Statement x' = x-3y y'= -2y There are two solutions of this system that lie on straight lines, in the sense that the ratio y(t)/x(t) is constant along each such solution. Find these lines and the corresponding solutions. Homework Equations None in particular that I can...

Homework Statement I'm trying to solve the following system of ODEs. \alpha = \alpha (r) \alpha ' + \frac{n-1}{2r} \alpha =0 \alpha '' + \frac{n-1}{r} \alpha ' = 0 The attempt at a solution The solution to the first one is \alpha = r^{\frac{-(n-1)}{2} The solution to the...

I have this question, but don't know how to even start. Suppose (M) is a linear system of 2 equations and 3 unknowns, where (2,-3,1) its solution. Suppose (O) is a matching homogeneous linear system, where (-1,1,1) and (1,0,1) its solutions. How can I find the general solution of (M)? I'm...

Hello all, i would like to ask you how can be solved this system: X'*X=A, where A (pxp) known Matrix and X(nxp) the matrix i want to compute. Thanks in advance

Hi community, I have a linear systems of equations (8x8), but the matriz's components are discrete. In this moment, I make values' all of components and I write them in 64 files of 150x6000. My question is How do you solve a linear systems of equations discrete?, I mean, How do I work with...

Homework Statement A line passes through (3,4). What is the maximum value of x+y? Homework Equations y = mx + bThe Attempt at a Solution So I set up a system of equations, m3+b =4; b = Y; mX + b = 0. Then I plugged my values for X and Y into m3+b = 4.. The weird thing is though...

Homework Statement let ui , ci \in Rn and A \in Mn(R) be such that AciT = uiT , i=1,2,...,n Suppose u1,u2,...,un are linearly independent. Show that c1,c2,...,cn are linearly independent Homework Equations N/A The Attempt at a Solution i was just learning the eigenvalue, eigenvector...

Homework Statement let x2 + x + 1 be the characteristic polynomial of matrix B find B5 using Cayley-Hamilton's Theorem Homework Equations The Attempt at a Solution from what i have learn, cayley hamilton theorem is something like this B2 + B + I =0 B(B+I)=I so, B-1 =...

Homework Statement let u1 , u2 , u3 \in R3 be such that Au1T = u1T , Au2T = \frac{1}{2}u2T , Au3T = \frac{1}{3}u3T Suppose u1 , u2 , u3 \neq 0 Show that u1 , u2 , u3 are linearly independent Homework Equations a1u1 + a2u2 + a3u3 = 0 a1 = a2 = a3 = 0 for it to become...

Homework Statement Show that rank(A+B) \leq rank(A) + rank (B) for every A,B \in Mm,n (Real) Homework Equations N/A The Attempt at a Solution i only know how to proof this rank(AB) \leq rank(A) or rank(B), and can this "rank(AB) \leq rank(A) or rank(B)" help me to...

Homework Statement Show that it is false If A is invertible and A-1 = adj A, then det A= 1 Homework Equations N/A The Attempt at a Solution ------------------------------------------------------ A is invertible iff A-1A = I implies det(A-1A) = det(I) implies det(A-1)det(A) = 1 implies...

Homework Statement let A (2x2 real matrices), If AB=BA for all B (2x2 real matrices) , show that A=bI2 for all b ( b are real numbers) Homework Equations N/A The Attempt at a Solution can anyone give me clue for this one too

Homework Statement Show that there are no A,B (2x2 and real number matrices) such that AB-BA=I2 Homework Equations N/A The Attempt at a Solution can anyone give me clue, how to prove this?

I'll make this post short. The problem just asks me to something in the form x'=Ax (A is a 2x2 of constants) and then describe the behavior of the solution as t approaches infinity. My solution is x=C1e-2t(2/3 1)T + C2e-t(1 1)T. Since both vectors are multiplied by 1/et, my solution...

Homework Statement Suppose that Gaussian Elimination gives the soluiton of a Linear System Ax=c as x = x0 + a1x1 + a2x2, where A is a 6X6 matrix and a1 and a2 are arbitrary. Is the matrix A invertible? Explain The Attempt at a Solution I simply explained that due to properties of an...

Homework Statement G(t) is nxn matrix depends on t. Show that solutions of x'=G(t)x form an n-dim subspace of C1(R+,Rn). The Attempt at a Solution So I can show closure, addition of solutions returns some combo inside R^n, and same with scalar multiplication. I need to show...

Homework Statement 1. a) If you have 22 coins consisting only of pennies, nickels, and dimes, and the coins have a total value of 100 cents, how many pennies, nickels, and dimes do you have? Also you have the same number of nickels and dimes. b) If you do not know that you have the same...

Homework Statement Find a third degree polynomial approximation for the general solution to the differential equation: \frac{d^{2}y}{dt^{2}} +3\frac{dy}{dt}+2y= ln(t+1) Homework Equations Power series expansion for ln(t+1) The Attempt at a Solution The system to the...

Homework Statement We are given a subspace of R^3 that is produced by the elements: (2,6,2) abd (6,2,2). We are asked to find (if any) a homogeneous linear system that has this subspace as solution set. Homework Equations The Attempt at a Solution 1)The subspace is 2...

Hello, I am currently working on a lab in which we are studying the behaviour of chain of metal bars attached together with nylon wire in such a way as to to mimic the ability of solids or liquids to transmit a wave. After studying the normal modes of the system as well as the quality...

Homework Statement x''+13y'-4x=6sint , y''-2x'-9y=0 The Attempt at a Solution I am not really sure how to solve this completely, but I have done this so far: (D^2-4)x + 13Dy - 6sint = 0 , (D^2-9)y - 2Dx = 0 then I hit a brick wall. Any help would be appreciated, thanks.

linear system: x + y +z = 2 2x + 3y+ 2z = 3 2x + 3y+ (a2 - 2)z = a+1 when reducing it to row echelon form, the last step looks like the following (if my calculations are right) 1 1 1 2 0 0 1 1 0, 1, a2-5, a-4 the question is to determine all values of a...

I wasn't sure if I should post this in homework help or here, since it qualifies as both, so if this is in the wrong section, let me know and I will delete and repost it accordingly. Anyway... The instructions are (verbatim): "show that the given system is almost linear near the origin and...

hi guys, can a time independent system model be controlled via a controller? I am assuming that we can obtain a solution for the model at each sample time, just assume that the model is of c= a*u type, i.e u is input which varing with the time. I am confsed...

Homework Statement Basically, the problem involves a linear system dx/dt = ax + by and dy/dt = -x - y, with a and b being parameters that can take on any real value. Basically, you go through this system for several values of a and b (I did -12 to 12) to find the state at various points...

Homework Statement I want to find certain coefficients \alpha_{uv} by minimizing a error function. In the end, I want to make a function of this, so iteration is not a problem. I want to estimate these coefficients to find the best estimate for f(x,y). Homework Equations The error...

Analytical Solution to this? -- linear system of ODES Hi All, It's been awhile since I've even attempted to solve something analytically, so before jumping back into the text. Does the following already have a common solution that I can find somewhere? Thanks, dx1/dt = A1 + B1x1...

I have a question: If the vectors of v & u are solutions of the nonhomogeneous linear system Ax=b, then ru+sv is a solution of the nonhomogeneous system for any real values of r and s. is this statement true? is this statement true for homogeneous systems too?

Hi, Does anyone knows how to prove that a potential transformer is a linear system or not? Can I use principle of superposition with time-domain impulse to prove it? Is there other ways other than the principle of superposition to prove linearity of a potential transformer? Is there a way to...

Homework Statement Hi , I would like to have some help with the question wheter or not a half wave rectifier ( one diode) is a linear cicuit. I would also like to know if the system is time invariant. The context is Fourier series. In a earlier question ,we wer asked to find the Fourier...

Solve the following linear system: ix + (1+i)y = i (1-i)x + y - iz = 1 iy + z = 1 I am getting nowhere with this. is there a trick to do these? I keep getting more and more variations of i. like i^2-1, and (1-i^2)-1 ix + (1+i)y=i (1-i)x + y-iz=1 y + z = 1 ix + (1+i)y = i i(1-i)x - (i^2-1)z =...

Homework Statement Hi all, I'm trying to implement the QR method for solving the linear system Ax = b. The QR factorization is achieved using Householder method. The Attempt at a Solution The main function is function x = lin_solve(A,b) [R,v] = householder(A); y = Qt_times_b(v,b); x...

Span of vectors in R3 Homework Statement u1 = (1,0,-1) u2 = (1,1,1) u3 = (3,1,-1) Determine whether the vectors span R^3. Homework Equations The Attempt at a Solution I know how to determine if the vectors span R^3(or maybe i dont). In this case checking if I can find a linear...

Homework Statement This isn't really homework help, I'm just trying to see if there is a "proper" way of doing this. Given \frac{dx}{dt} = x - y^2 \frac{dy}{dt} = x - 2y + x^2 show that the system is almost linear. Homework Equations The Attempt at a Solution...

Homework Statement Solve the system: dx/dt = 20 0 40 0 with initial value x(0) = -4 32 so x(t) = [] ?Homework Equations I'm not really positive how to do this and how to go about finding x(t). I've looked at wolfram mathematics, and tried following their definitions, but am a bit...

3x+3y+3z=3 x+y+z=-1 3 3 3 | 3 1 1 1 |-1 1 1 1 | 0 0 0 0 | 1 x = -y -z y = 1 Substitute y into x, x = -1 -z Let z = t, tER Then x = -1 -t, y = 1 The corresponding vector equation of the line intersection is: (x,y,z) = (-1, 1, 0) + t(-1, 0, 1) Does that look right...

I basically need to know how to test a system to see if it is linear or not. The professor gave us a "recipe" to check a system. I can kinda follow the recipe, but I would like to understand it, so I have reached out to other sources. The other sources deal with operators from the beginning...

never mind i got it :)

For this problem I don't think I am setting up the linear system right: Two tanks containing 500 gal of salt solution. Pure water pours into the top tank @ 5gal/s. Salt solution pours out of the bottom of the tank and into the tank bellow @ 5 gal/s. There is a drain @ the bottom of the second...

hello. please help! this is the problem: determine the value of h such that the matrix is the augmented matrix of a consistent linear system. 1 -3 -2 5 h -7 i tried replacing and scaling... but it seems there are always 2 variable in this. can you guys help me solve this problem?

Find the response of the of the linear system at rest y' + y = x , where x = sin(t) using the Fourier transform and formulas : Y(jw)=H(jw)X(jw) y(t)=h(t)*x(t) convolution

Just a quick question. If I have a system of linear equations, and I find a basis for the space of solutions, then each element in the basis should be a solution to the system right? Thanks!

Suppose A is a 3x3 matrix and y is a vector in \mathbb{R}^3 such that the equation Ax=y does not have a solution. Does there exist a vector z in \mathbb{R}^3 such that the equation Ax=z has a unique solution?

Here is the problem: X'\,=\,\left(\begin{array}{cc} 0 & 2 \\ -1 & 3 \end{array}\right)\,X\,+\left(\begin{array}{c} 2 \\ e^{-3t}\end{array}\right) Here is what I have: r_1\,=\,2,\,\,\,\,\,\,r_2\,=\,1 u_1'\,=\,-2\,e^{-2t}\,+2\,e^{-5t} u_2'\,=\,2\,e^{-t}\,-\,e^{-4t}...

One of the questions on a handout was this: Solve the following linear system: A) Precisely B) With a calculator. Since this linear system contains irrational numbers, how would you solve it "precisely"? How would the answer be any different than if a calculator was used? Do I just...

Hi, i have a question. Hope you guys can help~ Ques: Give a geometric explanation of why a homogeneous linear system consisting of 2 equations in 3 unknowns must have inifinitely many solutions. What are the possible numbers of solutions for a nonhomogeneous 2 x 3 linear system? Give a...