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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2
votes
2answers
74 views

How prove this equation have more one solution $x_{1}+x_{2}+\cdots+x_{n}=d,x_{1}x_{2}\cdots x_{n}=b$

Let $x_{i}\in \mathbb{Z},i=1,2,\ldots,n$, and such that $1\le x_{1}\le x_{2}\le\cdots\le x_{n}$. Show that $$\begin{cases} x_{1}+x_{2}+\cdots+x_{n}=d\\ x_{1}x_{2}\cdots x_{n}=b\\ b,d\in \mathbb{Z} ...
11
votes
1answer
146 views

Cyclic system of equations

Consider the system of equations $$ \begin{align*} x^2+(1-y)^2&=a\\ y^2+(1-z)^2&=b\\ z^2+(1-x)^2&=c\\ \end{align*} $$ Compute $x(1-x)$ in terms of $a,b,c$. Edit: The question should say ...
2
votes
2answers
67 views

How to determine the eigenvectors for this matrix

I have the matrix $$\left( \begin{array}{ccc} -\alpha & \beta \\ \beta/K & -\alpha/K \end{array} \right)$$ for which the eigenvalues are ...
2
votes
1answer
70 views

a system of finite difference equations

Let $a,b>0$ such that $ab<1$ consider the system$$x_{t+1}=x_ty_t+ay_t$$ $$y_{t+1}=x_ty_t+bx_t$$ I would like you to help me answer the following: find values $a$ and $b$ ​​for which the ...
0
votes
1answer
29 views

Gaussian elimination easily?

Let $$\left( {\matrix{ 1 & 0 & { - 3} \cr 0 & 2 & {\lambda + 3} \cr 0 & 0 & {5 - {\lambda ^2}/2 - 3\lambda /2} \cr } \left| {\matrix{ { - 3} \cr 2 ...
1
vote
1answer
52 views

Solving non-linear (convex) systems of equations

I have a system of non-linear equations that takes the following form \begin{align} \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots\\ y_n \end{array} \right] = \left[ \begin{array}{c} f_1({\bf ...
0
votes
3answers
38 views

Find the solutions set for a linear system

Let $$\left\{ {\matrix{ {a_1x + b_1y + c_1z = d_1} \cr {a_2x + b_2y + c_2z = d_2} \cr {a_3x + b_3y + c_3z = d_3} \cr } } \right.$$ It's given that the unique solution for the system ...
1
vote
4answers
74 views

The relation between $\det(A)$ and $Ax=b$

I wish to understand the the relation between $\det(A)$ and $Ax=b$. Hence, what are the solutions for $Ax=b$ (homogeneous and non-homogeneous) when $\det(A)=0$ and $\det(A)\ne 0$? So, all in all ...
2
votes
1answer
105 views

Three phase voltage system of polynomial equations

I'm working with the development of a product in the company where I work. This product measures three phase voltages and currents. I cannot change the circuit because it has been sold for a long time ...
0
votes
1answer
26 views

How do I modify a system of equations to receive unlimited solutions (SAT Question)

I am sorry that I don't have a specific question (it was on my sat make-up) but I remember a question that went something like 3x + 2y = 26 and another part of the system of equations that I don't ...
0
votes
1answer
51 views

How to solve these two differential equation?

I try to solve these two difference equation ; $$ \frac{dq}{dz} = -j\left(b_1q - kp\right),\\ \frac{dp}{dz} = -j\left(b_2p - kq\right) $$ where $j$ stands for $\sqrt{-1}$, and $b_1$ ,$b_2$ and k are ...
0
votes
0answers
29 views

Nondimensionalization of Coupled ODE

So what I'm messing around with are these two coupled ODES: $$\frac{dx}{dt}=\gamma x\left(1 - \frac{\alpha x+\beta y}{N}\right)$$ $$\frac{dy}{dt}=\theta y\left(1 - \frac{\alpha x+\beta ...
5
votes
1answer
97 views

When is the equation $Ax = b$ solvable in the integers?

Let $A$ be an $m\times n$ matrix with integer entries, $b$ a column-vector with $m$ integer entries. Suppose the equation $Ax = b$ has infinitely many solutions. It is clear that the general ...
0
votes
0answers
18 views

system of two quadratic equations with two variables

Is there a general way to solve exactly a system of this shape (the $a_i$ are constants): $$\begin{array}{cc}a_1x^2+a_2x+a_3y^2+a_4y+a_5=0\\ a_6xy+a_7x+a_8y+a_9=0 \end{array} $$ It comes from a ...
1
vote
1answer
23 views

Solving $x' = Ax$ for real $x$ where $A$ is a matrix with complex eigen values

I have the following linear differential equation system: $$x' = A x$$ where $$ A = \left( \begin{array}{ccc} 1 & 0 & 0 \\ 3 & 1 & -2 \\ 2 & 2 & 1 \end{array} \right) $$ I ...
1
vote
0answers
21 views

System of ODEs and DAE system

Let us consider the following system of ODEs: $$ y' = f(y,z),\quad z' = g(y,z),\quad y(0) = y_0,\;z(0)=z_0 $$ and the following one: $$ y' = f(y,z),\quad 0 = g(y,z), \quad y(0) = y_0. $$ $f$ and $g$ ...
0
votes
2answers
57 views

Find conditions on a, b, c, and d for which the following system has solutions:

Find conditions on $a$, $b$, $c$, and $d$ for which the following system has solutions: $$2x+4y+z+3w=a $$ $$-3x+y+2z-2w=b $$ $$12x+5y-4z+12w=c $$ $$13x+10y-z+13w=d$$ I got the system down to: ...
0
votes
1answer
21 views

Solutions of a system of linear equations with a parameter

I've come across a linear algebra problem that I'm not sure how to solve. It's a generic problem - I have to find the solutions of a system of equations dependent on a parameter. So, my first though ...
0
votes
0answers
55 views

Blowing-up a singular point

I have this system of ODEs: $$x'=-y+ \mu x(x^2+y^2)$$ $$y'=x+ \mu y(x^2+y^2)$$ I already find that in $\mathbb{R}^2$ the only singular point is $(0,0)$. So I have to blow-up the singularity to find ...
0
votes
1answer
33 views

Fastest way to compute minimal polynomial (for solving $x' = A x$, $A$ matrix)

In general, given a $3\times 3$ or $4\times 4$ matrix $A$ which doesn't have a lot of $0$ entries, what is the fastest or less error prone way to compute its minimal polynomial? More generally, I ...
0
votes
2answers
34 views

Solving $\left\{\begin{matrix}u'v''-u''v'=0 \\ R^2u'u''+v'v''=0 \end{matrix}\right.$.

Given that $u,v$ are functions of $t$, $R$ constant, solve $\left\{\begin{matrix}u'v''-u''v'=0 \\ R^2u'u''+v'v''=0 \end{matrix}\right.$. When trying to find geodesic on cylinder, I get this ...
0
votes
0answers
37 views

Solving solely continuous system of ode's with matlab

I'm working with the numerical integration of the system of differential equations, $\dot{x}=f(x)$ with the vectorfield, $f(x)$ being solely continuous. Examples of the systems which I'm working on ...
3
votes
3answers
100 views

Need help with simple system of differential equations

thanks to your help I advanced in computing differential equations, but now I encountered another problem I need help with - this time it is a system of differential equations: $$x_1'=-x_2$$ ...
1
vote
3answers
113 views

A system of $n$ equations , how does it behave for growing $n$?

I read about the system of $n$ equations in the link below. I wonder how it behaves for growing $n$. Does it converge ? http://math.eretrandre.org/tetrationforum/showthread.php?tid=889 Here it is ...
0
votes
0answers
17 views

What is a minimal equation system?

In the optimization seminar I have to study the quadratic linear ordering problem. And there is one lemma saying some equations form a 'minimal equation system' of a polytope. Does anybody know, what ...
1
vote
1answer
24 views

Unable to solve system of equations in Lagrange multiplier problem.

The problem: Find the right triangular prism of given volume and least area if the base is required to be a right triangle. As for parameters of the right triangular prism, $V$ is volume, $A$ is ...
1
vote
1answer
41 views

roots of system of nonlinear equations

I can't get any solutions beside when $x=0\vee y=0 \vee z=0$ $$yz-2x\lambda-2x\mu=0\tag{1}$$ $$xz-2y\mu=0\tag{2}$$ $$xy-4z\lambda =0\tag{3}$$ $$x^2+y^2=4\tag{4}$$ $$x^2+2z^2=3\tag{5}$$ Can you help ...
0
votes
1answer
39 views

Special equation solving

I would like to get x from the following function when the y is known and which + means If ...
0
votes
1answer
17 views

system of equations solving with only that information

Hi would would I go around to solve the following, there is no other information stat is given other than the fact that i have already expanded this from this $(25-y)(x+8)=523$ $25x-8y=323$
1
vote
1answer
28 views

Specific system of equations with multiplications

I'm facing a math problem that I thought easy, but I'm stuck with a solution that doesn't seem optimal. The problem is the following : I have "registers" which are the expanded representation of ...
3
votes
1answer
29 views

How to express $z'(t)$ and $w'(t)$ in terms of $z(t)$ and $w(t)$?

I have these functions: $x' (t) = −5x(t) + 2 y(t)$ $y' (t) = 2x(t) − 2y(t)$ where $x(0)=10$ and $y(0)=0$ I am also given these 2 functions: $z(t) = x(t) + 2y(t)$ $w(t) = −2x(t) + y(t)$ First ...
1
vote
0answers
66 views

Solving a system of linear ODEs

Based on my previous post, I have been stuck on this for a few hours now. I want to solve for $x$ and $y$ from the equation $$\frac{dx}{dt} + \frac{dy}{dt}=a-(b+c+d)y-bx.$$ The original two equations ...
1
vote
1answer
24 views

Solve system to find critical points.

Hi I have to find the stationary points for $$f(x)= x^4+y^4-(x-y)^2.$$ So far i founded the partial derivatives for $x$ and $y$. Next step is to solve this system to get my critical points: $$ ...
1
vote
1answer
67 views

Using Newton's method to solve a non-linear system of equations over complex numbers

I have a function $f(\bar{z},z)$ mapping from $\mathbb{C}^n \times \mathbb{C}^n \rightarrow \mathbb{C}^n$, which I would like to find the roots of numerically. Since it is nicely formulated in terms ...
0
votes
2answers
33 views

Make this system of 3 equations solvable for $x$, $y$ and $z$

I have the system of these three equations: $$ax = y+z$$ $$by = x+z$$ $$cz = x+y$$ How do I find all $a$, $b$ and $c$ for which the system has real, positive solutions for $x$, $y$ and $z$? As a ...
0
votes
2answers
19 views

What is wrong with this technique for proving skew lines?

We have the following set of lines: $$L_1: \frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-1}{-3}$$ $$L_2:\frac{x-3}{1}=\frac{y+4}{3}=\frac{z-2}{-7}$$ This leads to the following parametric equations: ...
1
vote
3answers
25 views

Simultaneous equations

I keep getting the following equation wrong: Firstly, I solve for y = x - 4, and substitute it in the second equation. Then once I get x from the second equation, I substite it back into the first ...
0
votes
1answer
75 views

Solving a system of equations using Newton's method

The following paper http://benisrael.net/Newton-MP.pdf provides a way to solve a system of equations using Newton's method. (The theorem begins at the end of page 2) I can't understand the ...
1
vote
1answer
50 views

An example on my book that asks for the basis of an eigenspace

Let $$ A = \begin{bmatrix}4&-1&6\\2&1&6\\2&-1&7\end{bmatrix}$$ An eigenvalue of A is 2. Find a basis for the corresponding eigenspace. Solution: Form $$A-2I = ...
0
votes
3answers
48 views

How does a row of zeros make a free variable in linear systems of equations?

I don't understand how a row of zeros gives a free variable when solving systems of linear equations. Here's an example matrix and let us say that we're trying to solve Ax=0: $$\left[ ...
0
votes
0answers
30 views

2 Coupled variable-coefficient linear ODEs

I am trying to solve the following boundary-value problem for functions f(x) and g(x): $$ f'' + p_1\left[ f(1)-f(x) \right] + a(x) g - p_2(1-x) -p_6 = 0,\\ (c_1+c_2p_1)g'' - c_3 g^{(iv)} -a(x) f'' =0. ...
3
votes
1answer
60 views

Existence of solutions for system of equations

I have a system of equations and was wondering whether there is any obvious reason that you find solutions for $e,f,c$ given a fixed $a \in \mathbb{R}$(which is true). So I don't want to solve this ...
1
vote
2answers
35 views

Finding a Lyapunov function for a given system of equations

I've got the following system of equations: $$ \begin{cases} x_1'=-8x_1^3-x_2 \\x_2'=-4x_2-4x_1^3 \end{cases} $$ I'm trying to check, if the equilibrium point in $(0,0)$ is stable or not. I am ...
2
votes
2answers
42 views

where did I go wrong in solving this sytem of nonlinear first-order ODEs?

To communicate my experience level and intent: I'm an undergraduate, this is not homework, I'm trying to write a physical simulation for fun and xp and am stuck just before (what looks to me like) the ...
-1
votes
2answers
39 views

Proof of axis of symmetry equation [closed]

Because quadratic functions are symmetrical how do you prove the axis of symmetry equation. $x=(-b/(2a))$
1
vote
0answers
19 views

How do I generate some sample solutions for an underdetermined system?

I have a system of 379 linear equations and 6325 unknowns. Does anyone know of a tool that can generate some (non-negative) solutions that satisfy this system? I know there are infinitely many, but it ...
0
votes
2answers
75 views

software to solve system of nonlinear equations

I am looking for a software to solve system of nonlinear equations. It would be great if the software can satisfy the following requirements It can support symbolic computation. It deals well with ...
0
votes
1answer
65 views

Help solve an equation

I'm preparing for the SAT and tripped over the following problem: $(x-8)(x-k) = x^2 - 5kx + m$ "In the equation above, k and m are constants. If the equation is true for all values of x, what is ...
0
votes
2answers
30 views

Classify critical point of linear system

For this linear system: $\dfrac{dx}{dt}=x+y-2$ $\dfrac{dy}{dt}=x-y-4$ I've found the critical point to be $(1,1)$ but now I want to classify it. How do I do it?
3
votes
2answers
63 views

A system of equations

Given three equations $x^2+y^2+xy=a$, $y^2+z^2+yz=b$ and $x^2+z^2+xz=c$, how can I solve for $x,y$ and $z$ in terms of $a,b$ and $c$?