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
23 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 ...
1
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1answer
22 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
16 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
1answer
44 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
43 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
55 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
25 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 + ...
0
votes
0answers
54 views

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

So I'm working on solving a couple of system of equations: $$ \text{Let} \ a,b \ \text {be a positive real number with} \ a\neq b \ \text{Solve the system:}$$ ...
0
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0answers
8 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
18 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?
0
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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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2answers
59 views

Simple problem, but confusing [closed]

At least, confusing for me. I have three times the age you had when I had the age you have. When you'll have the age I have, the sum of our ages will be 98 years. How old we are?
1
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2answers
30 views

Solve the equation, find the x

I need to find the x in thid equation. How is it done? a = x+1/x I've tried turning it into x² = 1-x times a, but it's not a system.. so.. any ideas?
1
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1answer
48 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
1
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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 ...
4
votes
1answer
209 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 ...
1
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2answers
35 views

How to solve the system of equations using Gaussian elimination, when there are more variables than equations? [closed]

How to solve the system of equations using Gaussian elimination, when there are more variables than equations? For example, this system has 5 variables and 3 equations; how to approach it? $$ ...
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0answers
31 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
46 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
votes
1answer
28 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. $n = [a, b]^T = [a_1+ja_2, b_1+jb_2]^T$ ...
0
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0answers
17 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
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1answer
21 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
66 views
+50

{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
23 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
votes
2answers
33 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
vote
1answer
25 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
votes
0answers
47 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
votes
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
34 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
36 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
64 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
21 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
19 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
votes
0answers
20 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
41 views

Solve the linear system by Gauss - Jordan elimination

$$ \begin{align} x& - y + 2z - w &= -1\\ 2x& + y - 2z - 2w &= -2\\ -x& + 2y - 4z + w &= 1\\ 3x& -3w &= -3 \end{align} $$ ...
0
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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
38 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
38 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
votes
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
vote
1answer
29 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
votes
4answers
362 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
40 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
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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, ...
3
votes
2answers
136 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
70 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 ...
0
votes
0answers
13 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 ...
1
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2answers
51 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. ...
2
votes
2answers
41 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
votes
4answers
109 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 ...