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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1answer
31 views

System of equations with symetric fractions

How to solve this system of equations? I tried to add and substract first and second equation but without any result. $$ \begin{cases} \dfrac{x}{y} + \dfrac{y}{z} + \dfrac{z}{x} = 3\\ \dfrac{y}{x} + ...
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0answers
37 views

Mathematical Economics/Environment

Bear with me - this is a long question. But I did do few of the parts, but I'm posting it because it seems necessary that you know what I previously did. Sorry for the "length"! Answers are given in ...
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0answers
44 views

Find three whole numbers with these characteristics

Find three whole numbers with the sum 147, knowing that the quotient of the second and first is 2 and the remainder 3 and the quotient of the third with the second is 3 and the remainder 2. Here's ...
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0answers
17 views

Symbol of operator and eigenvectors of symbol

In my opinion ,the symbol of operator is a polynomial that $\partial_i$ be replaced by $\xi_i$. And on the Wiki,there is some examples that the operator acts on one function $u$. But in the below ...
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0answers
18 views

SLE - vector arithmetic

Find all vectors arithm. (a,b) in R2 so that the solution of this system of linear equations: x*(1,2) + y*(2,1) = (a,b) is a multiple of the vector (a,b). The vector ((2b−a)/3,(2a−b)/3) is a multiple ...
0
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1answer
47 views

System of linear equations in C

Find all solutions for matrix depending on the parametres a,b ∈ C... With the usage of elementary row operations we can get to the reduced matrix Now, what is the appropriate way of the parametrical ...
1
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1answer
49 views

The linearization of a system and the derivative of operator.

Firstly, in red line 1 of the picture below,whether it means make a variable substitution $\widetilde {g}_{ij}=f(x)g_{ij}$? Because in my opinion, the linearization of something is to make a ...
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0answers
19 views

Solving a special system of N+1 equations

Let $\alpha$ and $\beta_i$ with $i=1,...,N$ be known real constants, with $0<\alpha<1$ and $0<\beta_i<1$ for all $i=1,...,N$. I need to solve the system of $N+1$ equations defined as $$ ...
1
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0answers
59 views

Moore-Penrose Inverse as least-squares solution

I'm trying to understand a conclusion in [1], [2]. There they state a definition and a theorem: Definition(5.2 in [1], 2.2 in [2]): For a general linear System $Ax=y$, we say that $\hat{x}$ is a ...
1
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1answer
46 views

Solving a system of equations - minimizing f

Completely stumped as to how to solve this problem -_- We'd appreciate any help at all: Suppose $f(x, y) = 2x^2 + 2xy + y^2$ and $g(x, y) = x^2 + y^2$ Show that minimizing $f$ with a constraint on ...
1
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1answer
33 views

Getting independent equations by differentiation

My question is related to the procedure used in the following paper: HEP paper. No need to even look into the physics, this question is strictly related to the solving of equation (27): ...
1
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0answers
28 views

Characteristic Variety of the Principal Symbol solves PDE system?

In the study of partial differential equations, it is often considered enough to analyze the principal symbols and their characteristic variety (see, ...
1
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2answers
32 views

When solving a simultaneous equation like this:

When solving a simultaneous equation like this: $2y - x = 4 $ $2x² + 3y² = x + 4y = 17 $ How do you express this second equation? I know how to solve simultaneous equations. I'm not just sure of ...
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2answers
43 views

If $A_{n \times n}x=b$ has no solutions then $Ax=0$ has infinitely many solutions

If $A$ is matrix of order $n \times n$ over an infinite field and $Ax=b$ has no solutions then $Ax=0$ has infinitely many solutions. Is that true?
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0answers
22 views

How to find the autocorrelation and spectral density of a given linear system?

A sample function of a stationary stochastic process $Y(t)$ with spectral density function $S_y (\omega)=[\delta(\omega- \omega_0 )+ \delta(\omega+ \omega_0)]$ is used to excite a linear fixed system ...
-2
votes
1answer
17 views

How to prove the following inequality holds: [closed]

Let $$y \geq -D$$$$ 0 \leq x < \frac{1}{D}$$ where $D > 0.$ How do I show that $$\frac{y}{1 + xy} \geq \frac{1}{x-\frac{1}{D}}$$
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2answers
41 views

Solving $\frac{dx}{dt}=-2x-2y, \frac{dy}{dt}=-2x+y$ with initial condition $(x(0), y(0)) = (1, 0)$

The course I am taking is using the text Differential Equations by Blanchard, Devaney, and Hall, and I want to solve the following problem: Solve $$\frac{dx}{dt}=-2x-2y, \quad ...
1
vote
2answers
96 views

Diophantine Equation : $x+y+z=3$ and $x^3+y^3+z^3=3$

Solve, in integers, the system of equations. $x+y+z=3$ $x^3+y^3+z^3=3$ I'm not sure how to approach this question, as I have only dealt with linear diophantine equations.
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2answers
33 views

System of non linear equations

$$\left\{\begin{array}{l} \ln(x+5)+y^2=10\\ x^2+y^2=9 \end{array}\right.$$ I have to solve this system of equations. Let us assume: $ x=ty$ The system becomes: $$\left\{\begin{array}{l} ...
1
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2answers
41 views

Laplce transform solution to this system of Nonlinear ODEs

I want to solve this system of advective-diffusive-reactive equations analytically: $$\left(\alpha - k_0c_B\right)c_A+v\frac{dc_A}{dx}-D\frac{d^2c_A}{dx^2} = f_A $$ $$\left(\alpha - ...
2
votes
1answer
34 views

How do I solve this 3 x 3 system of non-linear equations?

I have to solve this problem, but I am stucked $$y1 = \frac{x1}{x1 + x2} $$ $$y2 = \frac{x1 +x2}{x1 + x2 +x3} $$ $$y3 = {x1 + x2 +x3} $$ How do I solve for x1, x2, and x3? The best I coud do is ...
1
vote
1answer
45 views

A cyclic system of cubic equations

I would like to solve the following system of equations over the real numbers: $$\left\{ \begin{array}{rcl} x + y^2 + z^3 &=& 3\\ y + z^2 + x^3 &=& 3\\ z + x^2 + y^3 &=& 3\\ ...
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0answers
24 views

System realizability: What definition is correct?

Known that, sys realizability is given by: A system G is realizable if and only if the transfer matrix G(s) is a proper rational matrix. Out of the two statements below, which one is correct and ...
0
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2answers
41 views

Perform two iterations of Newton's Method on this system. $4{x_1}^2={x_2}^2$ and $4x_1{x_2}^2-x_1=1$.

Perform two iterations of Newton's Method on this system. Starting with $(0,1)$, $4{x_1}^2={x_2}^2$ and $4x_1{x_2}^2-x_1=1$. I'm not sure I understand "starting with $(0,1)$". I know how to use ...
1
vote
1answer
18 views

Maximum value of a variable from a system of 2 equations

From the following $2$ equations, find the maximum value of $d$. $a + b + c + d = 8$ and $ab + ac + ad + bc + bd + cd = 12$ How to go about with this problem? Please help. Thankyou.
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0answers
13 views

Problem with nonlinear equation system

I need to calculate two coefficients: k and n. This involves solving two equations for k and n: $$\frac{(8 \pi d)}{\lambda }{kn}=\frac{\text{$\triangle $I}}{I}$$ $$\text{$\triangle ...
0
votes
1answer
44 views

Using determinant approach to find values of a and b for a matrix system [closed]

Use the determinant approach to find all values of a and b for the system Ax=k... (system found in picture link) $$\begin{bmatrix} 1 & 0 & 1 \\ 0 & a & b \\ 0 & b & 1 ...
0
votes
1answer
75 views

When do the solutions to the linear system $Ax=b$ form a vector subspace?

When do the solutions to the linear system $Ax=b$ form a vector subspace? A) If and only if $A$ is invertible; B) if and only if $b=0$; C) if and only if $A$ is not invertible; D) if ...
1
vote
2answers
53 views

ODE system requires a trick

Let's consider a system of non-linear ODE: $$ x' = 1-x^{2}-y^{2} \\ y ' = 2xy$$ The final goal is to draw a phase portrait (of course, manually). The trouble is that this system, as i can suggest ...
4
votes
1answer
54 views

Evaluating an intriguing expression.

Let $x_1,x_2...x_{2014} \in R, \not= 1$ such that $$x_1+x_2...+\ x_{2014}=1$$ and $$\frac{x_1}{1-x_1}+\frac{x_2}{1-x_2}...+\frac{x_{2014}}{1-x_{2014}}=1$$ ...
0
votes
2answers
30 views

Solving a system of real-valued polynomials

How would i solve this system of equations $(x+y+z)^2 - 4 - 5yz = 0$ $(x+y+z)^2 - 4 - 5xz = 0$ $(x+y+z)^2 - 4 - 5xy = 0$
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votes
1answer
46 views

System of trigonometric equations

How can I solve this system of trigonometric equations for $0 \leq a\leq 2\pi$ and $0\leq b\leq2\pi$ $$\cos a + \cos (a+b) = 0$$ $$\cos b + \cos (a+b) = 0$$ the plot shows three points of ...
0
votes
0answers
16 views

Verification of the Inconsistency of a 4x4 System

This is a question from an old test that I'm using to get ready for my exam. Verify that the following linear system is inconsistent: \begin{array}{cccc|c} 1 & 1 & 1 & 1 & 1 \\ 2 ...
0
votes
1answer
38 views

Showing that three systems define the same behaviour

I have three input/state/output representations of the form $$\begin{cases}\frac{d}{dt}x=Ax+Bu \\ y=Cx\end{cases}$$ with the three systems given by: $$A_{1}=\begin{bmatrix} -1 & 0 \\ 0 & -2 ...
0
votes
2answers
75 views

Problem solving three equations using matrices.

Hi I'm not able to solve this system of equations, I use elementary row operations but it's pretty complicated, will you guys help me? $$-x-5y-5z=2$$ $$4x-5y+4z=19$$ $$x+5y-z=-20$$
1
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2answers
11 views

System of Equations with Square Pattern

Find 16x + 25y + 36z if: x + 4y + 9z = 10 4x + 9y + 16z = 120 9x + 16y + 25z = 1230 I tried using "brute force" and solving for each variable but the numbers are very large and messy ( I do not want ...
2
votes
2answers
37 views

Solution space of a linear system

Whats an example of a 2x3 matrix $A$, if possible such that the solution space of the linear system $Ax=0$ is $\mathbb R^3$? I know the zero matrix is one, but does there exist a non-zero matrix?
0
votes
1answer
71 views

Solving a system of equations with Cobb-Douglas production function

I have two equations and two unknowns in the following: $$p \alpha x_{1}^{\alpha-1}x_{2}^{\beta}-w_{1}=0,$$ $$p \beta x_{1}^{\alpha}x_{2}^{\beta-1}-w_{2}=0.$$ After solving I am supposed to get my ...
1
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0answers
43 views

Solving non-linear system of equations with Matlab

I encountered a non-linear system of equations that has to be solved. The system of equations can be written as: $$Ax + \exp(x) = b$$ with $b$ a known $N\times 1$ matrix, $A$ a known $N\times N$ ...
-1
votes
2answers
107 views

Consistent system of linear equation with exactly one solution

I'm given the following system of linear equations which is 3x3 $$ \left[\begin{array}{rrr|r} 1 & a+b & a-b & ab \\ 0 & a^2-9 & 0 & a-3 \\ 0 & 0 & b+2 ...
3
votes
3answers
75 views

There is a smart way to solve this 2x2 system of linear equations?

I was helping a high school student to study system of equations and he showed me this problem: \begin{align}\frac{x-a}{b} + \frac{y-b}{a} &= x-a \\ \frac{x+y-b}{a}+\frac{y+b}{b} &= 3 . ...
1
vote
1answer
48 views

Solution $(x,y)$ to $x^y=y^x=a$, $a>1$ being real.

I seem to have found a method to compute the solution $(x,y)$ to the equation, $x^y=y^x=a$ $a\geq 1$ where $a$ is real, by using limits. But I don't know if this is something new. Does there already ...
0
votes
1answer
55 views

Counting Siblings Word Problem: Linear Algebra Systems

Question: Alexandra and Brandon are brother and sister. We know that Alexandra has just as many brothers as sisters, and that Brandon has twice as many sisters as brothers. How many children are there ...
0
votes
1answer
93 views

polynomial curve fitting: higher order models' root mean square error does not decrease

I am trying to fit a curve for 15 data points. I started by creating a linear model and observing the root mean square difference, followed by quadratic, cubic and increasing the degree of polynomial ...
0
votes
1answer
46 views

What is the notation for a system of simultaneous equations?

Both in school and university, systems of simultaneous equations were denoted by a straight line in front of the equations (like a determinant, but no line after). Now I find out that both LaTeX and ...
1
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1answer
43 views

system of three equations with Cramer's rule

First of - sorry for my English. My math teacher gave me three tasks to complete, but I can't complete the second one. Here is the system: $$\begin{cases} x+y-z=3 \\ x-3y+2z=1 \\ ...
0
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2answers
33 views

When equating a rational function to zero, is there anything to be done with the denominator?

I am solving this equation: $$0 = \frac{2x-20-y}{30-2y+x}$$ I'm pretty sure that for this to equal zero I just need to solve the numerator, but is there anything I need to do with the ...
2
votes
2answers
32 views

isomorphic equations

W. Ross Ashby states in his book "An Introduction to Cybernetics" that the system: $\ x' = 1/2(x^2+y^2) + x*y + y$ $\ y' = 1/2(x^2+y^2) + x*y + x$ is isomorphic to the system: $\ u' = -u$ $\ ...
3
votes
1answer
46 views

Where is this converging to on $y=x$?

Well I was playing with graphs and I started plotting equations as the following: $$\underbrace{x+y}_{degree=1}=1 \tag{1}$$ $$\underbrace{x^2+y^2+xy}_{degree=2}+\underbrace{x+y}_{degree=1}=1 ...
3
votes
3answers
61 views

Prove that if $A$ is a symmetric matric then $A^3$ and $A^2-2A+I$ are symmetric matrices.

I am uncertain on how to approach this proof. For most everything I've encountered concerning symmetry, it has involved taking the transpose in order to show some property. Here, I'm not certain if ...