Linear system Definition and 149 Threads

during its annual picnic, a company supplies lemonade for all employees and their families. the picnic committee has purchased twice as many pint jugs as quart jugs and 8 fewer gallon jugs than quart jugs. how many jugs of each type are there if 22 gallons of lemonade were purchased? (there 2...

I have big problems with an equation system. It's been a long time since I worked with these type of problems and it would be wonderful if I could get an full solution of this or some similar problem. Decide for all real a and b, the number of solutions to the equation system. I...

I've found the characteristic equation of the system I'm trying to solve: $$ω^{4}m_{1}m_{2}-k(m_{1}+2m_{2})ω^{2}+k^{2}=0$$ I now need to find the eigenfrequencies, i.e. the two positive roots of this equation, and then find the corresponding eigenvectors. I've been OK with other examples...

I have attached the problem of interest. I think I am having trouble calculating the standard deviation for part a. D=A-B-C E(A)=10 E(B)=2 E(C)=2 sigma(A)=0.1 sigma(B)=0.05 sigma(C)=0.1 where sigma=standard deviation so to find SD...

\mathbb C: (1+i)x + 2y = 3, 3x + (1i)y = 2i I don't know how to go about this, am I supposed to do addition of complex number? Please help.

Let Ax = b be a linear system whose augmented matrix (A|b) has reduced row echelon form 1 2 0 3 1 ||-2 0 0 1 2 4 || 5 0 0 0 0 0 || 0 0 0 0 0 0 || 0a) Find all solutions to the system b)If a1= (1,1,3,4) and a3=...

Basically I don't know anyone in real life that can help me with this, so I need help checking to see if my answers are correct :) PART A 1) Using a graphing utility solve the following system of linear equations. Round your answer to the nearest hundredth. y = -4x+2 x - 2y = 10 My answer: x...

I have another question so please help me. here we go -- Consider the following linear system of ODE : X’ = -x – y Y’ = x + 3y Z’ = 4x + 6y - z Note that the matrix of this system is exactly the same as A = [ 1 -1 0 1 3 0 4 6 -1 ] (a) Study the stability of the fixed...

Homework Statement I have done this exercise, but I don't have a file with the solutions. COuld you please check it? Thank you in advance :) Given the following system: ##\lambda \in \mathbb{R}## ##x − z = \lambda## ##x + y + 2z + t = 0 ## ##y + 3z = ## ##x + z + t = 0## 1-find...

Hello everyone! I have a question on whether a system of equations can be classified as linear. I have the following matrix: \begin{equation} \left[ \begin{array}{c} S_t(1) \\ S_t(2) \\ \vdots \\ S_t(\omega_N) \end{array} \right] = \begin{bmatrix} f(x_1, x_2, 1) & f(x_2, x_3, 1) & \cdots &...

Solve the equation m\frac{d^{2}x}{dt^{2}} + c\frac{dx}{dt} + kx = (ax + b)^{2} + c^{2} for the constants m, c, k The right hand side a, b, and c are arbitrary digits. For me they are a = 2, b = 3, and c = 8. The problem recommends creating a linear system of equations for me to solve. This...

In linear algebra, you can have systems of differential equations represented by matrices. What does a "trajectory graph" of such a system show, exactly? And how can you draw one? What's the difference between such a trajectory-graph and an ordinary slope-field for a single linear...

Homework Statement X'=AXA=\left[\begin{matrix} 0 & 1 & 0 \\ -1 & 0 &0 \\0 & 0 & -1\end{matrix}\right] Homework Equations n/a The Attempt at a Solution The eigenvalues are -1, and \pm i. I also can see that the matrix A is already in the form A=\left[\begin{matrix} \alpha & \beta & 0 \\...

Here is the question: Here is a link to the question: How do you solve a pair of coupled differential equations where the matrix of coeffs has complex Eigenvalues? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hey guys, I'd assume that this will be a very easy answer. I need to clarify what is an inconsistent linear system. I've worked out my matrix and have achieved this form: x+0y+z+0w=0 0x+0y+z+w=0 0x+0y+0z+w=0 I know that an inconsistent linear system has no solution i.e 0=1. This is...

I know that the eigenvalue of a linear system is a scalar such that Ax=λx. I know many ways to find the eigenvalue of a linear system. But I'm pulling my hair out trying to figure out what it is actually telling me about the system. Can anyone give me a non-technical straight up answer on why...

Homework Statement In the proof of Lemma 3.6, what happens if there are no non-‘0 = 0’ equations? Homework Equations 3.6 Lemma For any homogeneous linear system there exist vectors B1,...,Bksuch that the solution set of the system is {c1 B1+..+ckBk|c1,..ck εR} where k is the number of...

Homework Statement Solve the following systems by either substitution or elimination: dx/dt = y dy/dt = -x + cos(2t) Homework Equations I know the solution is: x(t) = c_1cos(t) + c_2sin(t) - 1/3cos(2t) y(t) = -c_1sin(t) + c_2cos(t) + 2/3sin(2t) The Attempt at a Solution x' = [ 0 1; -1...

Hi there, I have a linear algebra question relating actually to control systems (applied differential equations) for the linear system {\dot{\vec{{x}}} = {\bf{A}}{\vec{{x}}} + {\bf{B}}}{\vec{{u}}}\\ \\ A \in \mathbb{R}^{ nxn }\\ B \in \mathbb{R}^{ nx1 }\\ In class, we...

Homework Statement I'm stuck on the following problem: A linear system has an output of G(\omega ) e^{-i \omega t} to an input signal of e^{-i\omega t} where omega is arbitrary. If the input signal has the form f(t) = \begin{cases} 0 \\ e^{-\lambda t} \end{cases} where lambda is a constant...

The question goes like this. Among all solutions that satisfy the homogeneous system x + 2y + z = 0 2x + 4y + z = 0 x + 2y − z = 0 determine those that also satisfy the nonlinear constraint y − xy = 2z I know that one of the solutions [0,0,0] but I'm not sure how to find the others. I row...

Homework Statement Consider the network of streets with intersections a,b,c,d and e below. The arrows indicate the direction of traffic flow along the oneway streets, and the numbers refer to the exact number of cars observed to enter or leave a,b,c,d and e during one minute. Each xi denotes...

Find the general solution to the following system of equations and indicate which variables are free and which are basic. Putting it in augmented matrix form to start we have: 1 -1 -1 4 | -3 1 0 -1/2 3 | -1 1 1 0 2 | 1 Now performing the following fundamental row operations: R1<-->R2...

Find the general solution to the following system of equations and indicate which variables are free and which are basic. x_1 + 4x_4 + 3 = x_2 + x_3 x_1 + 3x_4 + 1 = \frac{1}{2}x_3 x_1 + x_2 + 2x_4 = 1 Putting it in augmented matrix form to start we have: 1 -1 -1 4 | -3 1 0 -1/2...

So suppose you have a nice simple linear system dx/dt = a1x + b1y + c1 dy/dt = a2x + b2y + c2 and a critical point (x0, y0) ≠ (0,0). If you want to analyze the stability in the usual linear method, then I assume there should be some transformation to have the critical point at the origin. So is...

Hi, I have a problem from a textbook on control systems along with the solution, but I'm not certain how the answer was derived. The only thing I'm confused by is the method by which the system of equations was solved, which appears to be something similar to, but not quite, Cramer's rule...

Homework Statement A general system of linear equations is ax+by=e cx+dy=f where a,b,c,d,e,f are constant values. a)Use elimination to solve for x and y in terms of a,b,c,d,e,f. b)Are there any values that a,b,c,d,e,f cannot have?The Attempt at a Solution For part A, I got x=(e-f)/(a-c)...

Hello All: Suppose I have a completely known linear system: A*x=b. I know the matrix A, and an x and the associated RHS vector b (and it is non-trivial). Is there some tricky way to directly determine the inverse of A without performing an inversion by typical means (Gauss elimination, LU...

Hello Forum, a system of linear algebraic equations can have 1 solution, zero solutions, or infinite solutions. Can it ever have multiple, finite solutions? Why not? when the system has infinite solutions, are the equations representing all the same identical equation, i.e. they are...

Homework Statement I'm trying to solve #1 here: http://www.student.math.uwaterloo.ca/~math115/Exams/M115.FE.pdf The problem is: The Attempt at a Solution (a) At a=2, the slope is the same. I figure any value but 2 gives unique solutions. But I don't know if this is right. (b) At...

Homework Statement Solver for n and m in the following equations: 2n + 6m \equiv 2 (mod 10) n + m \equiv -2 (mod 10) Homework Equations The Attempt at a Solution I've worked through several of these problems prior, including ones in the book and most take the form: 2n + 3m = 3...

Suppose that the linear system Ax=b is given for some symmetric A, and it is known that vector c spans the null-space of A. How could one formally show that if b is not orthogonal to c, the solution to the system Ax=b does not exist? To remind you, the null-space of A contains all vectors u...

Hi folks, I'm hoping to get your opinions about something. If i were given two linear equations and needed to solve for x and y using the methods of "substitution" and "elimination", what algebraic structure should i use? I can solve the systems just fine, but I'm trying to "explain" each step...

Hi everyone, I'm currently taking an abstract Algebra course and need a little guidance with an analysis of solving a system of linear equations. We are given two linear equations and need to solve for x and y using the method of "substitution" and again using "elimination". However, we must...

Homework Statement Find all solutions for the following system: X^2-xy+2y^2=8 X^3-xy^2=0 2. Questions What steps could I take to solve this? I've tried just about everything I can think of. I don't know if I should solve the cubic equation for a variable and plug it in or what. I am...

Homework Statement Homework Equations An overtdetermined system - If m > n, then the linear system Ax = b is inconsistent for at least one vector b in ℝ^n. The Attempt at a Solution If m > n (more rows than columns), in which case the column vectors of A cannot span ℝ^m (fewer vectors...

Steepest descent for linear system what is the formula of steep descent to solve linear system can you give me a link

Hi, I have a general question about linear wave equation: Is solving the linear wave equation is equivalent to compute the output of a linear system where source is the input? Thanks in advanced! Chao

Show that if (Spectral radius) ρ(M)≥1 then there are x0 and c such that the iteration xk+1 = Mxk+c fails to converge I am very lost on how to solve this problem. All the literature I have been able to read up proves the converse of the statement. I am unable to crack this. Show that if A is...

Hello. I need to find a differential equation for a linear system, H, which is characterised by the impulse response h(t) = e-2t, where t denotes time. But I am not sure how to go about this. Would anyone be able to point me in the correct direction? Thanks in advance. Seán

Homework Statement Consider the system of equations \begin{eqnarray*} e_1 &=& Ak^p + Bh^q \\ e_2 &=& A(k/2)^p + Bh^q \\ e_3 &=& Ak^p + B(h/2)^q \\ e_4 &=& A(k/2)^p + B(h/2)^q \end{eqnarray*} Suppose that the e_i are known, as well as k and h. Find A, B, p, and q. Homework...

Homework Statement Determine the stability of the following linear system y(n) = 0.5x(n) +100x(n-2) - 20x(n-10) Homework Equations x(n) = 0.5\delta(n) S=\sum^{\infty}_{k=0}\left| h(k)\right| The Attempt at a Solution Z \left\{ 0.5x(n) +100x(n-2) - 20x(n-10) \right\} Z...

Homework Statement I'm stuck in a problem where I deduced a set of non linear equations. I must solve for A_0, A_1[/itex], x_0 and x_1. I just don't know how to tackle this. The system is: A_0+A_1=\frac{2}{3} A_0x_0+A_1x_1=0 A_0x_0^2+A_1x_1^2=\frac{2}{5} A_0x_0^3+A_1x_1^3=0...

Homework Statement Show how the following solution set: [x1,x2,x3,x4,x5,x6,x7,x8]^T =[1,-1,0,0,0,0,0,0]^T, [0,-1,1,0,0,0,0,0]^T,[0,0,0,1,-1,0,0,0]^T,[0,0,0,-1,0,1,0,0]^T,[0,0,0,0,-1,0,1,0]^T,[0,0,0,0,0,-1,0,1] is obtained from the two linear equations x1+x2+x3-x4-x5-x6-x7-x8=0 and...

The problem: "A commercial customer orders 81 gallons of paint that contains equal amounts of red paint, green paint, and blue paint - and hence, could be prepared by mixing 27 gallons of each. However, the store wishes to prepare this order by mixing three types of paint that are already...

1) Find a vector equation for the plane in R3(3D) with scalar equation 2x − 3y + z = 5 . First,I find three points on the plane and then I used one point as a fixed point in order to find two vectors on the plane by using two other points. Then, I tried to test whether the two vectors are...

Homework Statement Classify the fixed points of the following linear system and state whether they are stable or unstable \dot{x}=x + y \dot{y} = x + 3y Homework Equations The Attempt at a Solution Fixed point at dy/dx = 0/0. Therefore fixed point = (0,0) How does one test...

Homework Statement Verify that the given vector is the general solution of the corresponding homogeneous system and then solve the nonhomogenous system. Assume that t>0. tx' = |2 -1|x + |1- t^2| |3 -2| |2t | General solution: x = c1| 1|t + c2| 1|t^-1 | 1|...

Homework Statement Solve using an augmented matrix: 3r-2s+4t=6 2r+3s-5t=-8 5r-4s+3t=7 2. The attempt at a solution [3 -2 4 | 6] => [1 0 0 | x] [2 3 -5 |-8] => [0 1 0 | y] [5 -4 3 | 7] => [0 0 1 | z] I have successfully used 2x2 augmented matrices, but with 3x3 it seems like there are...

According to this, http://upload.wikimedia.org/math/5/8/2/582b41cd88284564c46e711cbbca55fa.png http://en.wikipedia.org/wiki/System_of_linear_equations#Homogeneous_systems A general solution to some linear system is a particular solution (P) + a homogeneous solution (H) My question: is...