Tagged Questions

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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0
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2answers
37 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
45 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
27 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
27 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
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
48 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
votes
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
votes
1answer
46 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
44 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
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
votes
4answers
421 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
vote
3answers
44 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, ...
3
votes
2answers
157 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
73 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
15 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
vote
2answers
69 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
111 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 ...
1
vote
1answer
34 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 ...
0
votes
0answers
24 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 ...
10
votes
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" ?
5
votes
2answers
95 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
votes
1answer
32 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 ...
1
vote
0answers
31 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 = ...
8
votes
1answer
71 views

Solving $x_1+x_2=x_3^2, x_2+x_3=x_4^2, x_3+x_4=x_5^2,x_4+x_5=x_1^2, x_5+x_1=x_2^2$ in reals

find answers of this system of equations in real numbers$$ \left\{ \begin{array}{c} x_1+x_2=x_3^2 \\ x_2+x_3=x_4^2 \\ x_3+x_4=x_5^2 \\ x_4+x_5=x_1^2 \\ x_5+x_1=x_2^2 \end{array} \right. ...
6
votes
2answers
116 views

Stability analysis for ODEs with non constant inputs

For a project, I have to deal with systems of ODE's with non constant input such as: $$\begin{cases}\dot x =I(t)x+x^2\\ \dot y=x\end{cases}$$ where I(t) is a random input (for example). In any case, ...
1
vote
0answers
23 views

continuation of thread connected with system of congruences

System of 3 linear congruences I read this subject and I have doubts. Why $x\equiv 25 \pmod{7^2} \implies x\equiv 4\pmod {7} $ ? $x\equiv 399\pmod{1089}$ Is equivalent to system: $x \equiv 399 ...
0
votes
1answer
84 views

Linear Algebra (Ax=B)

I am having some difficulty thinking about a certain concept in my linear notes. I will post below the theorem that is involved, Theorem: Let X$_0$ be a particular solution of the system AX = B ...
0
votes
6answers
313 views

How to solve a system of two linear equations with two unknowns?

How do I solve this system of equations? $$\begin{cases} 7(a+b)=b-a \\4(3a+2b)=b-8\end{cases}$$ Progress I tried both substitution and elimination, but when I set $a$ or $b$ free on one side, I ...
0
votes
1answer
47 views

How to find system of equations from solution space

I have to find homogeneous system of linear equations whose solution space is: V = span((1,-2,4,3),(1,-1,6,4),(3,-8,8,3)). First I found vectors were linearly dependent, so I discarded the third ...
2
votes
4answers
52 views

system of congruence - my approach

We have: $$k^3 + l^3 \equiv 0 \pmod{17}\\ k^2 + l^2 \equiv 0 \pmod{17} $$ And I get: $$k = 17n+r_k\\ l = 17m+r_l$$ And I analyzed possible rests respect to system of congruences. My result is: $$ ...
0
votes
2answers
41 views

Can one solve this system of qudratic equations unambigiously?

Given the parameters $p_1, p_2, p_3$ I want to know if the following system can be solved: $p_1 a + p_2 c + ef = 0\\ p_1 b + cd + p_3 f = 0\\ ab + p_2 d + p_3 f = 0\\ p_1^2 +a^2+b^2=1\\ ...
0
votes
0answers
28 views

Solving an equation with boundary conditions to find coefficients

I want to find the unknown constants in the function $f(x,y)=A(e^{-i.k_{x}x}+C_{1}x+C_{2})(e^{-i.k_{y}y}+C_{3}y+C_{4})$, using the following known boundary conditions and auxiliary equation ...
1
vote
1answer
42 views

Transforming a nonlinear system to a linear system

Suppose I have two points in $\mathbb{R}^2$ and I wish to find values of parameters $a$ and $b$ such that I obtain the power law $y=ax^b$ which goes through the two given points. I can solve the ...
0
votes
0answers
31 views

Solving a non-linear set of equations with non-exact constant values

I have a set of nonlinear equations which are related to a physical system. The constants of these equations (light hand side values-LHS) are determined through some measurement methods. It means that ...
0
votes
1answer
27 views

Find the roots of a polynomial in Matlab

I have a polynomial $f$ of order 15 and I want to find its roots. For solve(f==0), the answer is ...
3
votes
2answers
41 views

Finding equilibrium points of differential equation

Given the system $$ x'=xe^{y-3}$$ $$\space \space \space \space \space \space \space \space \space \space \space \space \space \space \space y'=2\sin(x)+3-y$$ Find the equilibrium points and decide ...
1
vote
1answer
33 views

Solving simultaneous equations with `min{}` function

I have following system of m number of simultaneous equations with min{} function. These equations are symmetric as well. ...
0
votes
1answer
25 views

Solving for a single variable in a quadratic system

I have a quadratic system of $n$ equations that looks like: $$ A_{ij}x_{j}y + B_{ij}x_{j}=0 $$ For $i=0...n$, where $A_{i,j}$ and $B_{ij}$ are integer matrices and sums over $j$ are implied. Is there ...
1
vote
0answers
67 views

How to find a linear equation with the same solution set?

I have this homework question that I solved, but it was so easy that I feel like I did something wrong. Can someone just confirm that my approach to this problem was correct? So, I have to find a ...
1
vote
1answer
32 views

How can I solve this set of linear coupled system?

Consider the matrix $A=\begin{bmatrix} -2k & k \\ k & -2k \end{bmatrix}$ .I have to solve this linear coupled system : $X'' = A.X$, where $X= \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix}$ ...
1
vote
1answer
31 views

Using jacobian to solve a nonlinear system of equations?

I have to solve a system of nonlinear equations using jacobian but I'm not sure how to solve for the solutions. I remember one of my friends doing $Ax = B$; where jacobian matrix was $A$, but im not ...
0
votes
4answers
54 views

Physics problem, stuck in algebra.

I end up with the equations; $$u=u_1' \cos(a)+u_2' \cos(b)$$ $$u_1' \sin(a)=u_2' \sin(b)$$ $$u^2=u_1'^2+u_2'^2$$ I have to show that $$a+b=\frac{\pi}{2}$$ $x'$ isn't the derivative of $x$, it's a ...
0
votes
0answers
42 views

Avoiding initial guess in Newton Method for nonlinear systems

Peace be upon you, I am solving the following system of equations for finding $\gamma$ and $\theta$, while I have about 18000 pairs of $\{c1,c2\}$ constants (i.e. I have about 18000 of such systems ...
2
votes
4answers
95 views

Solution to a system of nonlinear equations

Do you know any method to solve the following system of nonlinear equations ? $\begin{equation} 141,3829=A+\frac{B}{323}+5,78C+F323^{E}\\ 69,07645=A+\frac{B}{333}+5,81C+F333^{E}\\ ...
-2
votes
2answers
32 views

System of linear equation matrix? [duplicate]

How would I do this question. Determine the value(s) of $h$ such that the matrix is augmented of a consistent linear system. My matrix \begin{bmatrix} 1&h&4\\ 3&6&8 \end{bmatrix} I ...