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
42 views

Simple equations word problem

In a three-digit number, the difference between its hundreds digit and its tens digit is equal to the difference between its tens digit and its units digit. Also the sum of the digits is $9$. How many ...
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2answers
29 views

Huge linear system of equations with powers of $2$

I've got a large system of equations: $$ \begin{align*} (2^0)^na_n + (2^0)^{n-1}a_{n-1} + \cdots + (2^0)^1a_1 &= 4^0 \\ (2^1)^na_n + (2^1)^{n-1}a_{n-1} + \cdots + (2^1)^1a_1 &= 4^1 \\ \vdots\\ ...
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votes
1answer
65 views

Simplification of nasty expression

I have the following equation which I am trying to solve, $$ \frac{x^2}{y^2}- \frac{x^2}{y^4} -\frac{1}{2} \leq 0$$ Can anyone think of a way of simplifying the above, I don't think this is a form ...
2
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0answers
34 views

Nontrivial solutions for a system of equations

Consider $t:[0,1]^2\to R$ that is differentiable a.e. and satisfies conditions (i)-(ii): (i) $$ \int_0^1 \frac{\partial t}{\partial t_1}(x,y)f(y\mid x)\,dy=0, \quad \forall x\in[0,1] \\ \int_0^1 ...
1
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2answers
36 views

Property of a system of two inequalities

I have this system $$\begin{cases} a+b>1 \\ a-b>1 \end{cases}$$ can I sum the second inequality to the first getting $a>1$? Or this property can be used only equations?
2
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3answers
69 views

4 equations 3 unknowns

If I have 4 equations and 3 unknowns, I could solve for the 3 unknowns using the first 3. How does it ensure that the 4th equation is also satisfied? In this case, what should be the usual strategy to ...
1
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0answers
36 views

defining a system of differential equations

Given the system of equations $ \frac{d}{d t} j{\left (t \right )} = - \alpha j{\left (t \right )} + u{\left (t \right )} - \frac{d}{d t} x{\left (t \right )} $ $ \beta \frac{d}{d t} x{\left (t ...
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0answers
21 views

Approximating the Digamma fucntion near 1

Peace be upon you, I had the following system of equations to be solved \begin{align*} \begin{cases} \psi(\alpha)-\psi(\alpha+\beta)=c_1\\ \psi(\beta)-\psi(\alpha+\beta)=c_2 \end{cases} \end{align*} ...
0
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3answers
36 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.
1
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1answer
30 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
42 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 ...
1
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1answer
25 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 ...
3
votes
2answers
131 views

Trigonometric equation help is sought

A trigonometric equation is to be solved, the solution ($X=10^\circ$) is very clear but I need a proper method. $$\sin(60^\circ-2X)\sin(5X)=\sin(8X)\sin(3X).$$
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3answers
51 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 ...
3
votes
1answer
58 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 ...
1
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2answers
30 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
57 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
9 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 ...
0
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1answer
49 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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0answers
17 views

suggestion to finish my problem uncuople system PDE first order

I have $u_t+w_x=u$ and $w_t+u_x=0$ then I used $u=y+z$ and $w=y-z$ then we have $z_x+z_t=\dfrac{z+y}{2}$ $y_x+y_t=\dfrac{z-y}{2}$ how can I resolve it ?
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1answer
62 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
22 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
220 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
38 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 ...
0
votes
1answer
51 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 ...
0
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1answer
34 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
18 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 ...
1
vote
1answer
22 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
votes
1answer
80 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 $$\left\{\begin{array}{c}\sum_{i\in I_1}x_i=1\\\sum_{i\in I_2}x_i=1\\\vdots\\\sum_{i\in I_k}x_i=1\end{array}\right.$$ ...
0
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0answers
25 views

Goal programming exercise

First of all, i dont even know if this topic can be related to mathematics only, but i am reading this book about goal programming and i dont know what to to on the exercices, this is one of them: ...
0
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2answers
36 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 ...
1
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1answer
35 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
50 views

Combining two differential equations

I have two differential equations that are connected by an equation, $L_1\frac{d^2I_1}{dt^2} + \frac{1}{C_1}I_1=\frac{dV}{dt}$ $L_2\frac{d^2I_2}{dt^2} + \frac{1}{C_2}I_2=\frac{dV}{dt}$ $I_1+I_2=I$ ...
2
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0answers
16 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 ...
0
votes
2answers
36 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\\ ...
1
vote
3answers
43 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 ...
0
votes
1answer
67 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 ...
0
votes
2answers
26 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 $y'$ ...
0
votes
1answer
26 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 ...
0
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0answers
23 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
votes
1answer
47 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
27 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.
0
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1answer
44 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
votes
1answer
43 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.
0
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2answers
26 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 ...
1
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1answer
30 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
413 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 $A^2 = B^2$, ...
1
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3answers
43 views

System of Linear Equations - how many solutions?

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

Determine the number of real roots of the system.

Determine the number of real roots of the system,$1.$$x^3y - y^4 =a^2$ $2.$$x^2y+2xy^2+y^3=b^2$ where $a$ and $b$ are real parameters.
0
votes
0answers
32 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, ...