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
43 views

Can I find the value of $x & y$

Find x,y from N such as $x^{(2y)}=1560-x^{y}$.Is it possible to find the value of x and y only from one equation. please help me.I approached in different ways.But all my attempt went in vain.
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1answer
43 views

Solving a particular system in three variables

I am trying to analytically solve these equations for the three variables of $\theta$, $L_p$, and $R_c$. Matlab can not solve them! I am wondering if there is any solution for this at all? And how I ...
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1answer
100 views

Solving System of Equations using transformation rotation

I've never had to post the same question twice, but my last post is getting filled out with work and I'm going about it a different way so I figured i'd try a whole different question So This is the ...
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1answer
76 views

Translating verbal descriptions into algebraic expressions

I'm trying to solve the following problem but the result I'm getting is not logical given the data of the problem. Pat invested a total of \$30,000. Part of the money was invested in a money ...
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3answers
53 views

A simple system of equations

I'm trying to refresh my school math knowlegde and have trouble solving a simple system of equations: $\begin{cases} x + xy + y = -3,\\ x - xy + y = 1. \end{cases}$ I derive $y$ from the second: $y ...
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1answer
71 views

How do I solve $x=\log^e{(x+1)}$ analytically?

How do I solve the following, analytically? $$x=\log^e{(x+1)}$$ It looks like it should be simple, but whether I take the $e$th root of each side or take the $\log$ of each side (ending up with a ...
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2answers
41 views

how many solutions to non-linear simultaneous equations

I'm doing a Lagrange multiplier optimization problem, and I wound up with the following simultaneous equations: $2x + 1 -2\lambda x = 0$ $4y-2 \lambda y = 0$ $6z-2 \lambda z = 0$ $-x^2 - y^2 - z^2 + ...
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0answers
67 views

Solving Systems of equations for $(x,y)\in\mathbb {R}^2$

So I'm working on solving a couple of system of equations: $$ \text{Let} \ a,b \ \text {be a positive real number with} \ a\neq b \ \text{Solve the system:}$$ ...
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0answers
15 views

Can functions of differing order be meaningfully normalized?

I am attempting to understand how normalization works when applied to functions of differing magnitude. My understanding is that when you normalize you effective change the input ranges for a ...
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1answer
83 views

Point Parallel Form Describe Same Line as Point Normal Form

And that's how far I able to get, any suggestion how I can equate both (bold) equation or did I do totally wrong?
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1answer
91 views

$x^4-2x^3+x=y^4+3y^2+y$ in the set of integers

The task is to solve the equation $x^4-2x^3+x=y^4+3y^2+y$ in integers. I expect is has something to do with factorizing but have no concrete idea; any help? thx guys
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2answers
24 views

Show that there are constants $K$ and $\alpha$ such that $|(e^{At})_{ij}|\leq e^{-\alpha t}K$.

I want to prove that if all eigenvalues of $\textbf{A}$ in the sytem $\dot{\textbf{x}}=\textbf{Ax}$ have negative real parts then there exist constants $K$ and $\alpha$ such that ...
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2answers
260 views

Solved a quartic equation by dividing

I was asked to solve: $$x^4+2x^3-22x^2+2x+1 = 0$$ Without using differential calculus (Newton's Method). My Progress: Dividing by $x^2$, I get: $$x^2+2x-22+\frac{2}{x}+\frac{1}{x^2} = 0$$ $$x^2 ...
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0answers
75 views

Solving system of equations using mod math for a Hill cipher

I am having trouble eliminating these variables when I try to solve this system of equations. They may not even be the right equations, but it would be nice to see this worked out so I can try my next ...
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1answer
55 views

System of equations with parameter

I have been trying to solve this problem for a week now. It goes like this: Find all values of $a$ for which the system $$ \begin{cases} x^2-2x+y^2 = 1 \\[1ex] \dfrac{x+|x|}{y-a}=2 \end{cases} $$ has ...
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1answer
58 views

Which complex vector multiplied by its conjugate returns the identity matrix

I am trying to find (in case there is any) which complex vector $n$ of 2 dimensions, multiplied by its conjugate transpose, returns a diagonal matrix. $n = [a, b]^T = [a_1+ja_2, b_1+jb_2]^T$ ...
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0answers
20 views

Solving a quadratic system of equations for a single variable

I have a quadratic system of $n$ equations that looks like: $$ (A_{j}^{i}y + B_{j}^{i})x_{j}=0 $$ For $i=0...n$. $A_{i,j}$ and $B_{ij}$ are integer matrices and sums over $j$ are implied. $j$ runs ...
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1answer
33 views

For a linear function, the fiber of the output is the translate of the kernel by the input. (Trivial observation, proof needed.)

As you may already know, I am a newbie to linear algebra. I am supposed to prove that for every linear function between vector spaces, for every input, the fiber of the corresponding output equals the ...
2
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1answer
96 views

{0,1}-solutions for integer equations via lattice base reduction?

I would like to find $\{0,1\}$-solutions of a system of equations of the form $$\left\{\begin{array}{c}\sum_{i\in I_1}x_i=1\\\sum_{i\in I_2}x_i=1\\\vdots\\\sum_{i\in I_k}x_i=1\end{array}\right.$$ ...
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2answers
59 views

Hypersurface in $\mathbb P^n$ containing a linear subspace of dimension $r \geq n/2$ has singular points

I'm trying to prove that if I have a hypersurface $X = Z(F)$ (where $F \in K[x_0, \dots, x_n]_{d>1}$) which contains a linear subspace of dimension $r \geq n/2$ then there exists singular points on ...
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1answer
170 views

If we know nullspace of matrix, how to find reduced row echelon form of that matrix?

vectors u = [4 1 0 0] and v = [1 0 2 1] form a base of nullspace of matrix $$ A\in M_{5,4}(R) $$ Find a reduced row echelon form of Matrix A. Since $ n-r = dimN(A) $ we know we got two base ...
2
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0answers
90 views

Combining two differential equations

I have two differential equations that are connected by an equation, $L_1\frac{d^2I_1}{dt^2} + \frac{1}{C_1}I_1=\frac{dV}{dt}$ $L_2\frac{d^2I_2}{dt^2} + \frac{1}{C_2}I_2=\frac{dV}{dt}$ $I_1+I_2=I$ ...
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0answers
20 views

Existenence of the solution for a PDE-ODE system.

I have the PDE-ODE system below: $\frac{\partial c}{\partial t}= D \Delta c - \eta \nabla.(c\nabla v)+g(c,v)$ $\frac{dv}{dt}=-\alpha cv+\xi(c,v)$ with initial conditions and Neumann boundary ...
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2answers
54 views

critical points, differential equation

I have two differential equations and my assignment is to prove that this system have a unique stationary point. $$\begin{align} \frac{dx}{dt}&=a-(b+1)x+x^2 y\\ \frac{dy}{dt}&=bx-x^2y\\ ...
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3answers
64 views

Short question about the homogenous system

I am working on a text book problem for a intro linear course. But the solution is not in the back. I am looking to see if I understand it correctly. The question asks, " If A is a matrix, and the ...
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1answer
78 views

How to solve this system of 3 ODE?

I would like to know how to solve this system of differential equation. It consist of 3 ODEs, describing the behavior of an Induction Machine supplied with DC voltage. I a interested to derive the ...
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votes
2answers
41 views

Finding solutions for system of ODE

How does one find solutions for the system of differential equations of the form $$2x'-5y'=4y-x \\ 3x'-4y'=2x-y$$ ? All I can think of, is finding $x'+y' = 3x-5y$ and then substituting $x'$ or $y'$ ...
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1answer
86 views

I am thinking of a two digit number… (System of Equations Question)

I am thinking of a two digit number. If the digits of my number are reversed, the new number is 36 greater than my original number. If the tens digit of my original number is doubled and the units ...
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0answers
31 views

Polynomial systems - conditions for real solution

I was working on the computation of equilibrium points for dynamical systems and arrived in the following system of $n$ polynomials in the variables $(x_1,\ldots,x_n)$ \begin{equation*} ...
0
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1answer
64 views

Solve the linear system by Gauss - Jordan elimination

$$ \begin{align} x& - y + 2z - w &= -1\\ 2x& + y - 2z - 2w &= -2\\ -x& + 2y - 4z + w &= 1\\ 3x& -3w &= -3 \end{align} $$ ...
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1answer
29 views

System of equations with two unknowns

If I have three equations with two unknowns $(X, Y)$ , what should I do? I check that one is linearly dependent? and then I delete it. Thank you.
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1answer
93 views

Nonhomogeneous Linear Systems and Vector Space Solutions

Are there any nonhomogeneous linear systems with a solution set that forms a vector space? I know that, in order to be a vector space, a set must consists of a set V together with operations + (called ...
0
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1answer
60 views

Solve the linear system by Gaussian elimination

$\begin{cases}-2b+3c=1 \\ 3a+6b-3c=-2 \\ 6a+6b+3c=5\end{cases}$ I got an inconsistent linear system with the third row being 0 0 0 6. May someone please verify if I am right? I looked it over.
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2answers
29 views

Find solutions for an differential equation system

I have a differential equation system $x_1'(t) = -x_2(t)$ $x_2'(t) = -x_1(t)$ I see that I can write $\dot{x} = Ax$ where $A = \begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$ The complete ...
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1answer
40 views

Rational solutions to a system of equations

I have a system of equations $$\begin{align} xy + 3zw = 0; \\ xz + 2yw = 0; \\ xw + yz = 0. \\ \end{align}$$ Plugging it into a CAS, I see that all the rational solutions to this system have ...
5
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4answers
762 views

Linear Algebra - four “true or false” questions about matrices and linear systems

I'm reviewing for my linear algebra course, and have four "true or false" questions that I'm struggling to prove. I've included my approach to the solutions in brackets below them: 1) If $A^2 = B^2$, ...
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3answers
104 views

System of Linear Equations - how many solutions?

For which real values of t does the following system of linear equations: $$ \left\{ \begin{array}{c} tx_1 + x_2 + x_3 = 1 \\ x_1 + tx_2 + x_3 = 1 \\ x_1 + x_2 + tx_3 = 1 \end{array} \right. $$ ...
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0answers
38 views

Global existence of ode system without solving it explicity.asdf

Here is the ode system that I am looking at $x' = -y-z$ $y' = x + ay$ $z' = b + z(x-c)$ where a,b,c are positive constants. By the local existence theorem, I know that there is a local solution, ...
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2answers
196 views

System of Equations and Pumpkins? I Think Not.

Here is a challenge problem my math teacher gave to his pre-calculus class. I saw it. I attempted it. And I failed. It's sort of bothering me because my teacher said, "It's simpler than you're making ...
2
votes
1answer
85 views

Stability analysis for a system of two differential equations

I have this system of differential equations: \begin{equation} \frac{dx}{dt}=\alpha x-\beta xy\\ \frac{dy}{dt}=\beta xy-\gamma y \end{equation} I need to find the critical points and then do a ...
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0answers
18 views

How to insert a simplifier assumption in our equations set to find an ellipsoid equation

Regarding the below question: Finding equation of an ellipsoid two projected views (two ellipses) is not enough to solve the equation set and find a unique ellipsoid. For example, I chose a ...
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2answers
152 views

For the following system to be consistent, what must k not be equal to?

$6x - 4y + 4z = 5$ $9x - 6y + kz = -4$ $12x - 8y = -10$ Originally I just multiplied the first row by (3/2) and subtracted it from the second, which gives you a value of 6 for the answer. ...
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2answers
45 views

How to use differential equations to write $x(t)$ in terms of $y$ and $y_0$?

The equations are: $$ \left\{\begin{array}{rcrcl} x' & = & \mbox{}-a\,x & + & b\,xy \\ y' & = & c\,y & - & d\,xy \end{array}\right. $$ They want me to write an ...
2
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4answers
127 views

Solve system of equations with $\sin$ and $\cos$

Solve system of equations $\begin{cases} 3x^2 + \sin 2y - \cos y - 3 = 0 \\ x^3 - 3x - \sin y - \cos 2y + 3 = 0 \end{cases}$ I tried to use substitution $x = \cos t$ or sth, but I get literally ...
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1answer
36 views

How do I solve these systems of equations

How do I solve the following math problem? You have an 24 cm long string. Examine if you can cut in two parts and create a) Two squares b) Two circles whose total area is 20 cm². (The entire ...
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0answers
43 views

Matrix, Gauss-Jordan Method

I have a application problem for math and I am unable to get all my system of equations. I have two of three. Celia had one hour to spend at the athletic club, where she will jog, play handball, and ...
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6answers
1k views

what would be the way to solve a system of equations like this one?

Solve: $xy=-30$ $x+y=13$ {15, -2} is a particular solution, but, how would I know if is the only solution, or what would be the way to solve this without "guessing" ?
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2answers
101 views

Solve $x+3y=4y^3,y+3z=4z^3 ,z+3x=4x^3$ in reals

Find answers of this system of equations in reals$$ \left\{ \begin{array}{c} x+3y=4y^3 \\ y+3z=4z^3 \\ z+3x=4x^3 \end{array} \right. $$ Things O have done: summing these 3 equations give ...
0
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1answer
34 views

Solve $3$ variables using $4$ equations where $1$ equation contains $3$ variables

Suppose we are given the system of equations $$\alpha_1A+\beta_1B+\gamma_1C=x$$ $$\alpha_2A+\beta_2B+\gamma_2C+\theta_2D=y$$ $$\alpha_3A+\beta_3B+\gamma_3C+\theta_3D=z$$ where ...
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0answers
33 views

solution of the set of real non-linear equations

I have a set of real non-linear equations as following: \begin{equation} y_0 = f(y_0,y_1) \\ y_1 = g(y_0,y_1,y_2) \\ y_2 = g(y_1,y_2,y_3) \\ \vdots \\ y_{n-1} = g(y_{n-2},y_{n-1},y_n) \\ y_n = ...