This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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3answers
69 views

Solving a three variable equation

I have three given values, suppose a=1.86, b=2.6 and c=4.2. Now I have to figure out x,y,z such that $x\gt 0,y\gt 0$ and $z\gt 0$ $x+y+z=1$ $a*x\gt 1, b*y\gt 1$ and $cz\gt 1$ I need a ...
1
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1answer
76 views

solve system equation: $ 2a^2 - 1 = b, 2b^2 - 1 = c, 2c^2 - 1 = a $

I have this system equation: $$ 2a^2 - 1 = b $$ $$ 2b^2 - 1 = c $$ $$ 2c^2 - 1 = a $$ From system equation we see that $ a \neq 0 , b \neq 0, c \neq 0 $ , so : $ 2a^2 - 1 \neq 0 => a \neq ...
0
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1answer
33 views

Proving that if $ad-bc \neq 0$ then there is an unique solution to the linear system with 2 unknowns and 2 equations

Exercise: Prove that if $ad-bc \neq 0$, then the system $$ ax + by = j \\ cx + dy = k $$ has an unique solution. This is from the very first subsection of Hefferon's Linear Algebra, and also the ...
0
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1answer
25 views

Problem with Solve a Differential Equation

I Have a little problem . I wrote this function ( function describe dynamics of ball-hoop system): ...
3
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1answer
66 views

System of Equations: any solutions at all?

I am looking for any complex number solutions to the system of equations: $$\begin{align} |a|^2+|b|^2+|c|^2&=\frac13 \\ \bar{a}b+a\bar{c}+\bar{b}c&=\frac16 (2+\sqrt{3}i). \end{align}$$ Note ...
0
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0answers
21 views

Finding the Inverse of Polynomial Equations (Approximatly)

Assume one is given a set of two equations of the form: $$x(u,v) = u + a_1 u^2 + b_1 u v + c_1 v^2$$ $$y(u,v) = v + a_2 u^2 + b_2 u v + c_2 v^2$$ And one would like to find the inverse functions, ...
-3
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1answer
35 views

Solution of the equation… [closed]

How to find out the analytic solutions of the equation $1-4\sin^2\frac{\theta}{2}=\frac{\sin\theta(n-1)}{\sin\theta n}$ in the interval $(0, \pi)$? $n$ is an arbitrary integer constant.
1
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1answer
21 views

Positive solutions to a system of linear diophantine equations

A system of equations is $$x_1+x_2+x_3+x_4=b_1$$ $$x_1+x_5+x_6+x_7=b_2$$ $$x_2+x_5+x_7+x_8=b_3$$ $$x_3+x_6+x_8+x_{10}=b_4$$ $$x_4+x_7+x_9+x_{10}=b_5$$ $b_1,...,b_5$ and $x_1,...,x_{10}$ are positive ...
0
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2answers
47 views

Computer algebra system for solving systems of partial differential equations / PDEs [closed]

Looking for a symbolic computer algebra system software package, capable of symbolically solving systems of partial differential equations (PDEs). I am certain this can be done with Maple and ...
3
votes
0answers
80 views

System of symmetric equations

I was working on writing some problems for a contest, and I wrote the following system of equations: \begin{align*} x^2+yz&=259,\\ y^2+zx&=217,\\ z^2+xy&=203. \end{align*} Of course, ...
0
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0answers
10 views

Generalizing the algebraic nature of linear inconsistent system

I want to know whether solving any inconsistent linear system in any dimension end up in a similar manner that is $0 = a$ where a is non zero. For 2D, the only reason for inconsistent system can be ...
1
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1answer
20 views

Can this system of linear equations have infinite solutions?

$ax_1 + bx_2 + 2x_3 = 1$ $x_1 + x_2 + x_3 = 1$ I'm fairly sure that I cannot, however my exam prep question seems to suggest that it might (perhaps it's poorly worded).
1
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0answers
40 views

How To Solve This Non-Linear System (Ellipsoid-Plane-Cone Intersection)

Any help on how to solve this ellipsoid-plane-cone intersection problem or just even how to approach it will be greatly appreciated. All vectors are in $\mathbb{R}^3$ and I am trying to find ...
0
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2answers
20 views

Finding for which value of an unknown a linear system has a single solution

I have a system of linear equations (two equations, two variables) and an unknown coefficient a. I need to find which values of ...
1
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0answers
47 views

Polynomial roots finding algorithm

My initial problem is a parameter estimation problem that is solved by minimining a least-square criterion with the Gauss-Newton algorithm. However finding a good initial iterate is very tedious. ...
0
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3answers
23 views

Find the dimension of the vector space of solutions of $3 \times 4$ matrices $N$ where $N^{T}M=0$

Let $M$ be the $3 \times 4$ matrix displayed below $$ \begin{bmatrix} 1 &3&2&4\\ 2&4&3&5\\ 3&5&4&6\\ \end{bmatrix} $$ I want to find the dimension of the vector ...
0
votes
1answer
10 views

Solving a set of $N$ (what I hope may become) linear equations

When faced with $N$ beads on a string, I found the following equation $$-\omega^2A_p+2\omega_0^2A_p-\omega_0^2(A_{p+1}+A_{p-1})=0$$ Where $p=1,2,\dots,N$ and $A_0=A_{N+1}=0$ I know I can't solve for ...
1
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3answers
26 views

Which Coefficient will Make a 2-Variable Linear System Solvable?

This is most likely a pretty simple problem although my textbook doesn't quite explain how to solve it. I have a linear system with two equations and two variables (x and y) below: ...
0
votes
2answers
52 views

trouble with non-homogeneous ODE system… which method shall I use?

I am an undergrad statistics student and I am having troubles with non-homogeneous ODE systems. During my classes I went over just three methods for solving odes: Laplace transform, Fourier transform ...
0
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1answer
26 views

Amount of solutions added to a system of equations through the application of non-invertible operations.

Let's say we had a linear equation of the form $ax+b=c$ we then solve it for $x$ getting, let's say, $x=5$. Just for fun, let's pretend we haven't realized we had solved the problem, so we square ...
0
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0answers
51 views

How can I solve this variable-coefficient ODE system?

I originally have a linear, homogeneous, second-order variable coefficient ODE system of this form: $X''(x) = A(x)X(x)$, where $X(x) = $\begin{bmatrix} f(x) \\ g(x) \\ \end{bmatrix} ...
-1
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1answer
65 views

Solve system equation: $ \sqrt{a- \sqrt{b}} = \sqrt{c} - 1, \sqrt{b - \sqrt{c}} = \sqrt{a} - 1, \sqrt{c - \sqrt{a}} = \sqrt{b} - 1 $ [closed]

Can you help me how to solve this system equation: $$ \sqrt{a - \sqrt{b}} = \sqrt{c} - 1 $$ $$ \sqrt{b - \sqrt{c}} = \sqrt{a} - 1 $$ $$ \sqrt{c - \sqrt{a}} = \sqrt{b} - 1 $$
0
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1answer
38 views

system of equations 3 variables

I should find $A,B$ and $C$. I know answers but can't figure out how to solve it. Anyone? We are to find value of $x^4+y^4+z^4$ when $x, y$ and $z$ are real numbers which satisfy the following ...
0
votes
1answer
85 views

Solve the equation: $x^3+7x^2+16x+5=(1-2x)\sqrt[3]{-3x^2-7x+5}$

Solve the equation: $x^3+7x^2+16x+5=(1-2x)\sqrt[3]{-3x^2-7x+5}$ I used wolframalpha.com and get the solution: $x\in\{-3;2\sqrt2-3\}$ When $x=-3$, $\sqrt[3]{-3x^2-7x+5}=-1$ When $x=2\sqrt2-3$, ...
0
votes
1answer
24 views

Steady states of a system

How can I find the steady states? I am aware that the condition is to equal 0 but I am not able to say how many steady states there are... $$\begin{cases} \dot x=x-y^2 \\ \dot y= -x+2y-z^2 \\ \dot z= ...
1
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1answer
44 views

Lagrange multipliers problem with two constraints

Hi guys I am working with the following polynomial and I am trying to find the $\lambda , \mu$. I have a polynomial and I am trying to do Lagrange multipliers. Here is what I have. $f(x,y,z)= a ...
3
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0answers
46 views

Need help with this proof, I don't understand it , could anyone clarify some of the details. System of linear Differential equations.

$$(*)X'=A(t)X - system$$ $$(*)PX(\alpha)+QX(\beta)=0.$$-border conditions, where P,Q constant square matrices $n \times n $. Let $Y(t)$ be the fundamental matrix for the system $(*)$ normed for$ t= ...
0
votes
0answers
13 views

Inverse of pairing function

I am looking for the inverse of the unordered pairing function: $$ \langle x,y\rangle = xy + \left\lfloor \frac{\big( |x-y|-1 \big)^2}{4} \right\rfloor $$ where $x$ and $y$ are positive integers. ...
1
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1answer
24 views

How do you solve this system of equation?

if $J_x= \oint y^2 ds $ and $J_y= \oint x^2 ds $ and $J_{xy} = \oint xy ds $ how I can find $a$ and $b$? $$\left\{\begin{matrix} a.J_{xy}+b.J_x=-M_x\\ a.J_y+bJ_{xy}=M_y \end{matrix}\right.$$ ...
0
votes
1answer
12 views

Let the system $Ax=b$ be incompatible. Prove that $C^kx=0, C=[A,b]$ is determined for all $k\in \Bbb{N}$.

Let $A \in \Bbb{R}^{n \times (n-1) }$ be of rank $n-1$, let $b\in \Bbb{R}^n$. Let the system $Ax=b$ be incompatible. Prove that $C^kx=0, C=[A,b]$ is determined for all $k\in \Bbb{N}$. I can't use ...
0
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0answers
54 views

Exact solution to the given system of ODE 1

I'm trying to better understand basic neuroscience systems but I have almost no background in differential equations. Here's the standard leaky integrate-and-fire neuron with conductance based ...
3
votes
0answers
43 views

Properties of polynomials that are polynomial conditions on the coefficients

There are many occasions where we can check whether a (set of) polynomial(s) $f_i$ satisfies certain properties, simply by evaluating a fixed polynomial on the coefficients of the $f_i$. Many times, ...
1
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1answer
83 views

How to solve this system to model a simple betting system?

What I am asking is just for my personal curiosity. I was thinking about the betting system (ex. football). For example let's consider just this possibilities to bet: ...
0
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0answers
41 views

Solving the linear system $XL + L^TX = M$ efficiently

I'm wondering of an efficient way to solve the following system for the symmetric matrix $X$, given a positive semi-definite matrix $S$ and any matrix $M$: $$ LL^T = S $$ $$ XL + L^TX = M $$ $$ (XL) + ...
3
votes
1answer
190 views

Solution of an equation and a system of inequalities

Consider an integer $n \geq 1$, a positive real number $A$ and a collection of nonnegative real numbers $\{a_{i,j}\}$ defined for $(i,j) \in \{1,\cdots,n\}^2$. I want to find necessary and sufficient ...
4
votes
1answer
74 views

Solve the equations $\|Av\|=1/\|A^{-1}w\|$, $\|w\|=1$

I'm sorry if my question is rather stupid, but I have a brainfreeze right now. I want to prove that, for every $A\in GL(2,\mathbb{R})$ and for every $v\in \mathbb{R}^2$, $\|v\|=1$, I can find $w\in ...
1
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1answer
41 views

Using linear algebra (e.g. matrix) methods to solve a system of linear inequalities

Say we have the equation $Ax>b$, where $A$ is an M-by-N matrix, $b$ is a known vector of length N, x is an unknown vector of length N, and the inequality sign means that each element of $Ax$ is ...
0
votes
1answer
37 views

How do I find such matrices $X_{1},\ldots,X_{9} \in \mathrm{M}_{2}(\mathbb{Z}) $?

Is there someone who can give at a least an idea for solving this problem? Determine the matrices $ X_{1} , X_{2} , ..., X_{9} \in \mathrm{M}_{2}(\mathbb{Z})$ such that: $$(X_{1})^{4} + ...
1
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1answer
27 views

Linear System - Laplace - Determinant

Can somebody help me? I need to find the determinant of the related matrix with Laplace's method. What is the easiest way to find it? $x+y-z+w=1\\ x+2y+z-w=-1\\ y+2z-2w=-2\\ kx+3z=0$ Thank you for ...
2
votes
2answers
96 views

Can every statement be solved by mathematical induction ? (see details below)

I have the following equation system : $$\sum_{i=1}^n a_i^2 = n $$ $$\sum_{i=1}^n a_i=n$$ here the solution is only $a_i$ =1 . Can it be solved by mathematical induction ? I have tried , but have ...
3
votes
1answer
53 views

Is there an equation to describe translation and rotation?

Suppose a free rod, $l=2r$, is hit on a tip T and translates with $v= 1r/s$ and at the same time rotates with angular velocity $\omega= 1rad/s$. Is there an equation that can determine the position of ...
1
vote
1answer
24 views

How to calculate the intersection points of the same implicit curve in parametric form?

Take the following parametric equation of an implicit curve as an example: $$ \left\{\quad \begin{array}{rl} x=& \dfrac{27}{14} \sin 2 t+\dfrac{15}{14} \sin 3 t \\ y=& \dfrac{27}{14} \cos 2 ...
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1answer
46 views

Solving Systems of Equations ( Binomial * Trinomial )

This is not a homework question; rather a review for a Mechanical Engineering Board Exam. I need to find an efficient way to solve equations of these types: ...
1
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1answer
37 views

How do I solve trigonometrical simultaneous equations?

(Note: this question has elements of physics in it but I am looking for a solution to the purely mathematical side of it.) In trying to work out the resultant velocity and angle of an elastic ...
0
votes
2answers
23 views

System of equations that I'm having trouble with

$a/(x+y) - b/(x-y) = 1$ $b/(x+y) + a/(x-y) = (b^2-a^2)/2ab$ The answer to the values of $x$ and $y$ are given as $x=a-b, y=a+b$. How is that achieved?
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1answer
32 views

General solution of the system of equations

It seems like an easy question to solve but could not figure it out: If it is known that the following system of equations have a solution $x = x_1(t)$, where $x_1(t)$ is a second order polynomial ...
1
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0answers
12 views

Enforcing additional constraints in linear equation

In a finite element context, I come up with a sparse "stiffness matrix" $A$ and a corresponding RHS $b$. The goal is now to solve $$Au = b$$ Where $u$ is a coefficient vector of the solution. Now I ...
0
votes
0answers
35 views

multiple parabolas repeated hotizontally

I've been trying to write/find an equation which gives me ability to introduce dips on a parabolic graph on demand, basically, change a constant value or add a piece of equation to the original one to ...
1
vote
2answers
47 views

Finding particular solution to inhomogeneous system of differential equations

I am asked to find the general solution set of the following system of differential equations: $$\begin{cases} x' = 3x -2y-2 \\ y' = 6x-4y-1 \end{cases} $$ I found the general solution set of the ...
1
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0answers
35 views

Solving System of Linear Equations

These are the two known equations: $$\frac{(I_2+I_3)-(I_1+I_4)}{I_1+I_2+I_3+I_4} = \frac{2x}{L}$$ $$\frac{(I_2+I_4)-(I_1+I_3)}{I_1+I_2+I_3+I_4} = \frac{2y}{L}$$ where I know the values of $(x,y,L)$. ...