System of equations Definition and 276 Threads

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 I have been trying to solve this system of equations, I need to find for which values of k the system has infinite number of solutions, no solution and a single solution. I did some work, and found that for k=0 and k=1 there are infinite number of solutions and for k=-2 there is no...

Homework Statement i kick a ball with an initial velocity of 18m/s. there is a wall at 8m that has a height of 1.5 meters. whith what angle should i kick the ball so that it bearly passes the wall? Homework Equations first equation: hf= 1/2gt^2+vit+hi second equation: V=Δx/t The...

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 Solve the following system of equations: 2x1 - 2x2 -3x3 = -2 3x1 -3x2 -2x3 + 5x4 = 7 x1 - x2 -2x3 -x4 = -3 Homework Equations The Attempt at a Solution Ok so I solved the system and got: x1 -x2 = 5 x3 = 4 x4 = 0 so I've got a point (5,0,4,0) but...

This problem is not schoolwork, it is from "The Mathematics of Poker". I have three equations based off a 3x3 Rock, Paper, Scissors payout table where winning with scissors is given a +2 payout instead of +1. Homework Statement Find the solution to the system of equations Homework...

I'm not entirely sure if this belongs in the linear algebra section, but here goes: suppose I have two equations: b = d + e c = e*d I have described b and c in terms of e and d. Is it possible to solve for e and d in terms of b and c? Can anyone provide some possible techniques...

Solve the following system of equations in real numbers:$\sqrt{x^2-2x+6}\cdot \log_{3}(6-y) =x$$\sqrt{y^2-2y+6}\cdot \log_{3}(6-z)=y$$\sqrt{z^2-2z+6}\cdot\log_{3}(6-x)=z .$

I have a personal project I'm working on that involves calibrating some values from a sensor input. So far I've been doing the calibrations in a very tedious manner but I'd like to write a program to solve the calibration for me. Very long story very short, this basically boils down to the...

I've been dabbling with linear algebra lately and on the MIT OCW course for linear algebra, the professor talks about a column representation of a system of linear equations. For example, you teaches you to represent a 2x + 3y = 4 5x + 7y = 9 as a x [\stackrel{2}{5}] + y...

Hello, How would you discuss this system of equations by Gauss's method? \begin{bmatrix}{x}&{y}&{(m-1)z}&{1}\\{x}&{(m-1)y}&{z}&{m-1}\\{(m-1)x}&{y}&{z}&{m+2}\end{bmatrix} NOTE: the last column are the independent terms Thank you very much

Homework Statement A system of two equations with 3 variables is given. x + 2y +z = 1 3x - 4y = 2 calculate a thrird equation and add it to the system. the resulting system must have one and only one solution. Homework Equations The Attempt at a Solution my guess is...

we have to write a code to solve system of equations by writing them in matricies (tridiagonal matrix) form ... the first step is to enter the coefficients of the variables (r1,r2,r3,...) and then the answers to the equations (b1,b2,b3,...) by using array , and print the equations in the form...

How can i solve system of equations , if x,y,z\in \left[0,\frac{\pi}{2}\right)\begin{cases}\tan x+\sin y+\sin z = 3x\\\sin x+\tan y+\sin z = 3y\\\sin x+\sin y+\tan z = 3z\end{cases}

If a\;,b\;,x\;,y satisfy \begin{Bmatrix} ax+by=4\\\\ ax^2+by^2=-3 \\\\ ax^3+by^3=-3 \\\\ \end{Bmatrix}. Then (2x-1)(2y-1)=

Hello guys I need an advice on this one... A is a matrix of 4X8, and b is a vector of 4X1. It is known that the system Ax=b has infinite number of solutions. Which statement is correct ? a. rank(A)=4 b. rank(A)>4 c. rank(A|b)=rank(A) d. rank(A|b)=3 e. rank(A|b)>rank(A) my intuition say c...

Homework Statement Using Kirchhoff's rules, calculate the current in R1 with the directions indicated in the figure above. Assume that R1 = 1.00kΩ, R2 = 3.00kΩ, R3 = 5.00kΩ, E1 = 75.0V, E2 = 65.0V and E3 = 85.0V. Homework Equations Kirchhoff's rules The Attempt at a Solution Using...

Homework Statement Find the base and dimension of a system of equations: 3x1 - 5x2 + 2x3 + 4x4 = 0 7x1 - 4x2 + 1x3 + 3x4 = 0 5x1 + 7x2 - 4x3 - 6x4 = 0 2. The attempt at a solution Written in matrix form: 3 -5 2 4 7 -4 1 3 5 7 -4 -6 What I get: 11 -3 0 2 7 -4 1 3...

Hey Pf, I'm working on precalculus review and I have found myself stumped by a question. Homework Statement A rectangular field is enclosed by 600m of fencing. A second rectangular field, which is alongside a river, has the same area and is also enclosed by 600m of fencing. However, this...

Hi, I have a set of vectors that I would like to solve for in a nonlinear system of equations. I have tried to use scipy.fsolve to solve the system, but without success. I believe the problem is that scipy expects the same number of inputs as outputs. I have a 12x1 input vector, but I can...

I've been fooling around with the Fibonacci sequence for some time and I thought it would be interesting to see what would happen if I made the coefficients in a three variable system of equations follow that sequence. The results are intriguing and enigmatic. I discovered the following...

Homework Statement Ok I have been struggling a lot with this problem and I hope some of you might be able to help me out. Let's take this image: http://img822.imageshack.us/img822/3828/capturelqe.png All these dots labeled x1 to x25 are temperature points. All the dots along the edges of...

Hello Everyone, I am new to the forum, but I am kind of at a loss and I could use a little guidance. I currently have an assignment where we are given a traffic circle, with 4 on ramps and 4 off ramps (labeled a through h) which are constants. We are then given the traffic flow in between...

I'm looking for an algorithm to create a very simple (2 equations, 2 unknowns) linear system of equations that consists purely of integers. Specifically, a way to create a system of equations of integers and knowing that it can only be solved by integer answers, without actually solving it...

Homework Statement I'm currently implementing an algorithm in Matlab, however, I've hit a bump, I'm trying to solve the following system of equations: Known variables = a, b, c, d[complex] Unknown variabls = fs, fd, fv, alpha My problem is what to do with the |alpha| since I can't get...

Homework Statement Consider the following system of equations da/dt = -kab, db/dt = kab, a(0) = a0, b(0) = b0. Solve these equations exactly. Homework Equations The Attempt at a Solution I added them together to get d(a+b)/dt = 0 which implies a + b = a0 + b0. Therefore a =...

Homework Statement 1 1 1 | 2 0 5 2 | 12 0 -4 8 | 0 Answer: 100 | -3 010 | 2 001 | 1 Homework Equations The Attempt at a Solution How did they get the answer? I went over how to do 2x2 w/ someone but 3x3 seems different. Basically this is how I'm...

why does adding equations solve the system of equations? I've taken matrix algebra but, to be honest, was too bashful to ask such a simple question. :P

I am struggling with whether or not to define the following system as coupled: Using LaTeX (reload if it doesn't display properly) \ddot{x}+A*x=0 \ddot{y}+A*y=0 \ddot{z}+A*z=0 where A is a known constant equal to A=\sqrt{x^2+y^2+z^2} So, what do you think?

Homework Statement Solve the following system using Gauss-Jordan Elimination x - y + 2z - w = -1 2x + y - 2z - 2w = -2 -x + 2y - 4z + w = 1 3x + 0y + 0z - 3w = -3 The Attempt at a Solution I first wanted to ask what the difference between Gauss Jordan Elimination and Gaussian...

Homework Statement Is it possible to solve this system of equations using matrices? x^2 + y^2 = 42 x+3y+2y^2=6 Homework Equations The Attempt at a Solution I solved the system of equations using the following MATLAB code. I'm kind of confused by the results. Are there two x values...

Hi, the following linear algebra question is causing trouble for me: For which values of k does the following system of equations have a) a unique solution, b) infinite solutions, and c) no solutions? [ 1 0 3 | 0 ] [ 0 1 1 | 1 ] [ -1 1 k | k ] I know that having a unique...

Homework Statement Find the general solution for the following systems of equations, a solution to the initial value problem and plot the phase portrait. --> this is in matrix formx' = 1 2 0 3 all multiplied by x. also, x(0) = 2 -1 Homework Equations Determinant, etc.The Attempt at...

Homework Statement Hi there, I'm working on a simple model vehicle (powered by a twisted rubber band) applying torque to a drive wheel. I just want to understand the loads going through the member bodies. I've mocked up the enclosed free body diagrams and attempted to outline the systems...

Homework Statement As illustrated, a ball of mass m_1=0.25 kg and velocity V_(0_1=+5.00 m/s) collides head on with a ball of mass m_2=0.8 kg that is initially at rest. No external forces act on the balls. If the collision is elastic, what are the velocities of the balls after they collide...

Homework Statement sU-1+U-V=0 sV-2-U+V=(2/s) Homework Equations N/A The Attempt at a Solution the solutions are U=(s+1)/s^2 V=(2s+1)/s^2 but I just keep getting complicated polynomials that I don't seem to be able to factor. If someone could show me how this particular one...

Homework Statement 2x + 2y = 10 (2x)2 + (2y)2 = 68 Homework Equations The Attempt at a Solution If I divide them, I'm right back where I started to: 2x+ 2y = 6.8 I can't subtract or substitute either because that turns into a mess. Thanks for any help.

Homework Statement Solve the initial value problem | x'=x+y | y'=-x+y x(0)=y(0)=1 Homework Equations N/A The Attempt at a Solution This is actually a solved problem with a too many details missing. You have to set up the equation as | sX(s)-x(0)=X(s)+Y(s) |...

Homework Statement 4/x - 3/y=0 6/x +3/2y = 2 so I can make my own variables up. U= 4/x V= 3/y my problem is, how do I convert that on the second equation would 6/x turn into 1.5U and 3/2y turn into 1/V?

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...

Homework Statement Solve the system of equations for Bx = 0. Where B is the following matrix: [ 5 -1 ] [ 2 2 ] [ 1 4 ] and the x is some vector I am assuming.. is it: [ x1 ] [ x2 ] Homework Equations The Attempt at a Solution So what I figured was that I should do this...

Homework Statement Consider a linear system of four equations with three unknowns. We are told that the system has a unique solution. What does the rref of the co efficient matrix look like? Homework Equations The Attempt at a Solution When it says "unique solution" I'm going to...

if in a system of linear equations we have lesser number of linear equations than the number of variables then is the number of solutions set to the system always infinite ?

Homework Statement There are two forces P and Q that are applied to a crate, with their respective magnitudes 100 and 200 N. One is applied at an angle upward with angle theta, and one is applied at an angle downward with angle phi. Both have positive horizontal components and the sum of the...

how know how to do tis question determine the value a for which the resulting linear system has i) no solution ii)a unique solution iii)infinitely many solution x+y+z=3 x+2y+z=3 x+y+(a^2-8)z=a

N integer that satisfies I mean, the system has solution with x >0 and y < 0 a) {-2,2} b) {0,1} c) {6,7} d) {-3,-1,2}

Hi there, I have a system of 2n equations. n of these unknowns can be expressed explicitly in terms of the remaining n. The resulting n x n matrix is more dense than the original 2n x 2n and the original 2n x 2n system has some desired properties like diagonal dominance etc. So, should I...

2x+3y = 7, -> equation1 2x^2-3y^2 = -25; -> equation2 first of all tell me the type of equations first i solve for y equation 1 y = (-2x +7)/3 now what should i do ?

Homework Statement Solve for x and y .5= (x-40)/(x-y) and .5=(40-y)/(x-y) Homework Equations The Attempt at a Solution I have been trying to solve this system of equations for hours and I can't seem to get it. Can anyone please give it a shot and see what they get? I'm sure I...

Homework Statement Im trying to find local min and max values. So I have fx and fy. I need to find critical points by setting them equal to 0 4x^3-4y=0 and 4y^3-4x=0 Homework Equations 4x^3-4y=0 and 4y^3-4x=0 are fx and fy respectively The Attempt at a Solution I...