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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23 views

Can maple solve a nonlinear system of equations?

I have a system of equations, see below. I wonder if it is possible to solve this for $x,y, \gamma$ (the others are known) in a computer program for ex. maple? I do not wanna spend time doing this by ...
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2answers
37 views

solving system of equations involving imaginary numbers

What are the values of $a,b,c$ given the system of equations given below: $a+b+ab=i$ $b+c+bc=2i$ $c+a+ac=3i$
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1answer
9 views

Solution space for quadratic equations with nilpotent matrices

Let ${\bf w}\in\mathbb{R}^3$ and ${\bf N}\in\mathbb{R}^{3\times 3}$ be a nilpotent matrix with degree 3. Consider the following system of quadratic equations, $$ \begin{align} {\bf w}^\top{\bf w} ...
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1answer
10 views

Need some help with applying specific boundary conditions to b-spline system of equations

I'm building a package for B-spline interpolation in Julia, and I've come across a boundary condition that I want to implement but can't wrap my head around how to do it (mathematically). Basically, ...
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0answers
27 views

How to solve system of equilibrium probability state equations

I have started studying markov chains where i have these statistical equilibrium probability state equations.These equations are solved for a particular case $s_1=4,a_1=5,s_2=2, a_2=1$ and a 15*15 ...
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1answer
27 views

Geometric progression, two equations problem

We have two equations: $$1. \ a_1 + a_2 + a_3 = 21$$ $$2. \ a_1^2 + a_2^2 + a_3^2 = 189$$ Answer should by $a_1$, $a_2$ and $a_3$. How the title says, these 3 elements are part of geometric ...
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0answers
11 views

Solution to system of multivariate quadratic equations

I aim to find a vector ${\bf w}\in\mathbb{R}^N$ such that it solves the following system of quadratic equations, $$\forall i,j\quad {\bf w}^\top {\bf A}^{ij}{\bf w} = B_{ij}$$ where ${\bf ...
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0answers
32 views

How to solve the Probability Markov chain system of equations

I have this system of equations from a 2-D Markov chain (see the figure. How can i calculate the coefficient matrix, state probability vector and the constant vector from this system of equations. ...
2
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2answers
53 views

How do I deal with a floor function is a system of equations?

How would one solve an equation with a floor function in it: \begin{cases} y=12(x-\lfloor x \rfloor) \\ x=12(y-\lfloor y \rfloor) \end{cases} Maybe an algebraic method could be used?
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2answers
54 views

Solve equation of inverse functions

I have two different functions $y_1=f_1(x)$ and $y_2=f_2(x)$, both invertible but quite complex. I am able to find their inverse functions numerically, i.e. $f^{-1}_1(x)$ and $f^{-1}_2(x)$, by ...
0
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1answer
18 views

systems of equations with variables

I have the following problem in my homework Suppose a, b, are two constant paramaters such that the system below is consistent for any values of f and g. What can you say about the numbers a ...
2
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1answer
34 views

why does matlab give me a negative number?

I have the following problem A steel company has four different types of scrap metal (called Typ-1 to Typ-4) with the following compositions per unit of volume They need to determine the volumes ...
0
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2answers
28 views

System of linear equations - Resolution

$$ \left( \begin{matrix} \pi_1 & \pi_2 & \pi_3 \end{matrix} \right) = \left( \begin{matrix} \pi_1 & \pi_2 & \pi_3 \end{matrix} \right) \begin{bmatrix} 0.6 & 0.3 & ...
0
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2answers
23 views

Finding the general solution of a system of linear equations

so I've come across this question in preparation for an exam: Let $A$ be a $4\times 4$ matrix where $rank(A)=3$. The vectors $(1,2,0,-1),(0,2,1,1)$ are solutions to the system ...
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0answers
17 views

Parametric solutions to underdetermined system of nonlinear (product) equations

I have a system of equations where the left hand side is a constant and the right hand side is a product of some subset of $n$ variables. $$c=\prod_{i\in K} x_{i}$$ Where $K$ is some subset of the ...
0
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1answer
48 views

Singular solutions of a system of nonlinear 2nd order ODEs

I'm faced with the following nonlinear 2nd order system of ODEs: $$ \phi''(r)+\frac{4r^3-1}{r^4-r}\phi'(r)+\frac{r^2 h(r)^2+2r(r^3-1)}{(r^3-1)^2}\phi(r)=0, \\ ...
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0answers
8 views

Are there multiple solutions to this system of (two) equations? How can I know?

I have two equations: $$N_sc_s + p_s L =N_s \gamma^sw$$ and $$\frac{(1+g)N_s c_s}{\gamma} + \frac{(1+h)p_s L}{(1+n)\gamma} = N_s \gamma^s w$$ Where the variables are $c_s, p_s$. Obviously One way for ...
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0answers
17 views

satellites attitude determination TRIAD - how are orbital reference frame vectors constructed?

I posted this same question on space.stackexchange but never received any answer. So I am posting here hoping to get an answer as this is a quite mathematical topic. I am trying to fully understand ...
0
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1answer
19 views

Addition vs. Substitution method for Linear Systems of Equations with Parameters

I thought that solving a 2x2 linear system of equations using either the substitution method or the addition method (adding the two equations to eliminate a variable, then using the substitution ...
0
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2answers
33 views

How to solve $8x^3-6x+6xy^2=0=4y^3-4y+6xy^2$

How can I solve this system? $$ \left\{\begin{matrix} 8x^3-6x+6xy^2=0\\ 4y^3-4y+6xy^2=0 \end{matrix}\right. $$ I do $$ \left\{\begin{matrix} 8x^3-6x+6xy^2=0\\ 4y^3-4y+6xy^2=0 \end{matrix}\right. ...
3
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1answer
97 views
+100

Find elevator height given rope length?

This question is deceptively difficult. I feel like it's probably some classic example somewhere, but I'm not sure how to describe it in enough detail to get valid results in searching online. ...
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3answers
61 views

$17x+11y \equiv 7 \pmod {29}$ and $13x+10y \equiv 8 \pmod {29}$. What are x and y?

Congruency question: if $17x+11y \equiv 7 \pmod {29}$ and $13x+10y \equiv 8 \pmod {29}$, we need to find $x$ and $y$. There may be more than one answer. Not sure how to go about this; any help ...
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1answer
26 views

Inequalities (System) (solving it)

Solve the system of inequalities and indicate all the integers which are in the solution set: \begin{align*} 3−2a&<13 \\ 5a&<17 \end{align*} I solved it then i realized it said ...
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3answers
57 views

Solve nonlinear system of equations

Solve the system of equations $$\begin{cases}163-400z\sin{x}&=0\\-135z+85\cos{x}+61&=0\end{cases}$$ What is the best way of going about this? I rearranged the second equation for $z$ and ...
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0answers
14 views

Disadvantages of Taylor series method

There is method called Taylor series method to solve non linear equations iteratively. I am interested to know ,what are the disadvantages of using this method to solve. General Idea any one please?
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2answers
26 views

Evaluating condition for no roots using gauss jordan elimination

Find the number of values of $k$ for which the system of equations has no solution: $$(k+1)x+8y=4k$$ $$kx+(k+3)y=3k-1$$ This is the augmented matrix: $$\begin{bmatrix} k+1 & 8 & 4k ...
1
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0answers
48 views

Simultaneous equation with 6 equations, 6 unknows and a degre of 5

How do I solve this simultaneous $$a + b + c = 2\to (1)$$ $$ax + by + cz = 0\to (2)$$ $$ax^2 + by^2 + cz^2 = \frac{2}{3}\to (3)$$ $$ax^3 + by^3 + cz^3 = 0\to (4)$$ $$ax^4 + by^4 + cz^4 = ...
0
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1answer
30 views

General solution of a system of equations given a set of specific solutions

I'm pretty sure I did this right but I'd just like to check to make sure - I've been presented with the following problem: Given a non-homogenous system of equations with 4 variables so that the ...
1
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0answers
26 views

On a max-min problem from an exam.

I have asked a different question on the same exercise (from an exam) a couple weeks ago, I hope it is acceptable to have a different question on the same exercise, I searched the Meta and it seems ...
0
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2answers
42 views

When solving linear equations what does ${0x_n = 0}$ mean? What if the system is used to find Nash equilibrium?

When solving systems of linear equations one sometimes gets result like ${0x_n = 0}$ what does it mean for solving the system? Is it error on part of the solver or just feature of the assignment? ...
0
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1answer
39 views

show the Wronskian is constant

Let $p,q : \Bbb{R} \to \Bbb{R^n}$ and $H:\Bbb{R^n}\times \Bbb{R^n} \to \Bbb{R} $ and the hamiltonian system: $$ \begin{cases} \dot p = - \frac{\partial H}{\partial q} \\ \dot q = \frac{\partial ...
8
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1answer
104 views

Solve: $x = (x-\frac{1}{x}) ^ {1/9} + (1-\frac{1}{x})^{1/9}$

Solve: $$x = \left(x-\frac{1}{x}\right) ^ {1/9} + \left(1-\frac{1}{x}\right)^{1/9}$$ Simplifying, $$x^{10/9} = (x^2-1)^{1/9}+(x-1)^{1/9}$$ I don't know how to start. Any hint will be helpful.
0
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0answers
15 views

range of $\phi$ in given trigonometric equation

Let $\theta,\phi\in[0,2π]$ be such that $2\cos(\theta)(1-\sin(\phi)=\sin^2\theta(tan(\theta/2)+\cot(\theta/2))\cos\phi-1,\tan(2π-\theta)>0,-1<\sin(\theta)<\sqrt{3}/2$ then $\phi$ cannot ...
0
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1answer
35 views

Simultaneous equation with summation and square - how to solve?

$\mathbf{p}$ is a vector with dimension: $x \times 1$ $\mathbf{d}$ is a vector with dimension: $1 \times y$ $\mathbf{V}$ is a matrix with dimension: $x \times y$ $y \geq x$ $\mathbf{d}$ and ...
0
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0answers
19 views

Prove that the solutions of ODE system are globally defined

Consider the folloing ODE system: $$x'(t)= A(t) x(t)+ b(t)$$ $$x(t_0)=x_0$$ Show that the solutions of the system are globally defined. Hint: We have to use gronwall inequality lemma. Could ...
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2answers
62 views

Solve a system of two equations with cubic radicals

Solve the following system of equations ($x,y \in \Bbb R$): $$\begin{cases} (8x-13)y&=(x+1)\sqrt[3]{3y-2}-7x \\ (y-1)x^2+(8y+7)x&=y^2+12y+(x+1)\sqrt[3]{3y-2}. \end{cases}$$ I think this ...
3
votes
2answers
36 views

Calculations with an exponentially-weighted moving average

I need help figuring out the following formula: Where: CTLy = yesterdays CTL TSS = current Training Stress Score TC_c = your CTL Time Constant Now I have TSS, thats a number between 20-500 ...
-1
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0answers
67 views

Show that there is a limit cycle in the dynamical system

I have the dynamical system \begin{align} \dot{x}_1 & = -x_2+x_1(1-x_1^2-x_2^2), \\ \dot{x}_2 & = x_1 + x_2(1-x_1^2-x_2^2) \end{align} With the initial conditions $x_1(0)=x_{10}$ and ...
1
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3answers
49 views

what is the fastest way to solve equations having more than two variables of 1 degree?

Suppose I have four equations for four variables $$a+b+c+d=0$$ $$5a+3b+2c+6d=10$$ $$12a+21b+c+4d=30$$ $$2a+3b+4c+5d=40$$ Now what is the fastest way to find a, b, c and d? I know of elimination and ...
0
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1answer
27 views

overflow, round-off error

a) If the following function is written in a program, in what range of x would overflow or zero divide originated from round-off error occur? $f(x) = \frac{1}{1-tanh(x)}$ Assume that the ...
0
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1answer
23 views

Linear Algebra Systems of Equations

I'm just starting out, so please bear with me. While solving systems of equations in linear algebra, can you straight-up add, if two factors cancel? My problem: $$x_1 + 3x_2 -x_3 +x_4 +2x_5 = ...
4
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2answers
246 views

Is there any easy way to solve two equations with three unknowns?

Is there a way to solve the below simultaneous equations? One possible solution is $a_1=20.0948$, $a_2=10.0948$, $a_3=6.3448$. The variables are actually dual variables of the binding constraints. ...
2
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2answers
44 views

Solving for the positions of vertices of 3 line segments

I have 3 line segments of lengths p,q,r joined at their ends. Let's call the vertices A, B, C, and D. Suppose D is fixed at the origin. Suppose that A is constrained to move only in the Y direction. ...
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2answers
32 views

Find all $n$ such that $m = an$ or $m =\dfrac{n}{a}$

$a$ is the 1st digit (from the left) of a $3$-digit number $n$. We get the number $m$ by removing a from $n$ and putting it on the right of the unit-digit. For example, the number $123$ becomes $231$. ...
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0answers
25 views

Companion matrix of bivariate polynomial

A polynomial in one variable can be expressed as a companion matrix, of which the eigenvalues are the roots of the polynomial and which can be found by using e.g. QR decomposition or power iteration. ...
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1answer
26 views

Triple Simultaneous Equations not resolving the Equation for a Quadratic Function

so I'm doing this math problem for my Calculus I course in college. Here is a screenshot of the problem: Graph 1 (click here to view); the prompt is "Find an expression for the quadratic function ...
2
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1answer
39 views

Linear systems of equations and vector spaces

I'm looking for references that explicitly (and in an accesible way: -I come from engineering-) handle the connection between solving a linear system of equations and the abstract geometry involved.
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0answers
20 views

How to rewrite a system of two non-linear equations in order to make evident a property of the solution

I know this is non-general and may look uninteresting but asking is worth a try. I have the following system of two non-linear equations (in two unknowns x and y and two parameters a and p) that I ...
0
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1answer
21 views

Why Non Linear equations put equal to zero in Newton Raphson Mehotd

While solving non linear equations we put them equal to zero in Newton-Raphson Method.Why we do that? Any Idea?
1
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1answer
52 views

Launching a Plaintext Attack against Affine Cipher

Update 2 Being new to the world of Stack Exchange I did not realize that there exists a site solely devoted to cryptography. In light of this, I hope someone could help me migrate this question to ...