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
27 views

Product of uncommon real roots?

The product of uncommon real roots of the two polynomials $p(x)=x^4+2x^3-8x^2-6x+15$ And $q(x)=x^3+4x^2-x-10$ My attempt was to form an equation of form $p(x)+\lambda q(x)=0$ ...
1
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2answers
45 views

How to find the union&intersection of two lines by their equations?

I will try to be as clear as possible concerning my confusion, and I will use some examples(several ones). Case number 1. Assume two equations(in cartesian form) of two planes. $2x+2y-5z+2=0$ and $...
0
votes
0answers
33 views

Creating a homogeneous system of linear equations that has no solution?

I was given a question related to finding a $\lambda$ value for a homogeneous system of linear equations not to have any solution. This $\lambda$ was among the coefficients matrix (if considering the ...
0
votes
2answers
66 views

Eliminate $x_1,x_2,y_1,y_2,c$ from the following equations

I need to eliminate $x_1,x_2,y_1,y_2,c$ from the following equations.What would be the correct ( and quick ) technique to do so? $x_1y_1=1$ $y_1=4x_1+c$ $x_2y_2=1$ $y_2=4x_2+c$ ...
-1
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1answer
31 views

System of equations involving sum of any 7 numbers in a list of 8 positive integers

Let $a_1, a_2, ... , a_8$ be positive integers. It was discovered that sum of any 7 numbers from this list can only yield $56, 58, 61, 63, 64, 65, $ or $66$. What is the largest number on this list? ...
1
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2answers
78 views

The number of irrational roots of $(x^2 -3x +1)(x^2 +3x +2)(x^2 -9x + 20) = -30$ is___?

The number of irrational roots of $(x^2 -3x +1)(x^2 +3x +2)(x^2 -9x + 20) = -30$ is___? My Approach : Multiplying the above equation and then apply Descartis rule is very lengthy method. Also ...
0
votes
3answers
40 views

Solving polynomial equations given some constraints

I want to solve a polynomial equation but I know that it can have exactly one root. Is there some method to solve these kinds of problems. for example- $$A(1+x)^4 + B(1+x)^3 +C(1+x)^2 + D(1+x) +E=0$$...
0
votes
1answer
19 views

intersection of a line (certain direction) and a circle

I need to calculate (previously) the point where a ball will touch the inside of a circle (for a game I'm developing). So I have two equations, one of the direction of the ball, and another of the ...
0
votes
1answer
29 views

Error propagation - implicit functions

I have a little problem that I should solve quickly and I'm a little bit on pressure, so that any help/tip would be of great help. I have two nonlinear equations with two unknown variables x and y ...
1
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3answers
49 views

Solving Electric and Magnetic Fields for Charged Particle Path

I am using the Lorentz Force Equation and the electric-cross-magnetic field velocity equation] to solve for the E and B fields given the known path of a particle moving in 3D. So with that I have ...
0
votes
1answer
41 views

You own $19.75 in dimes and quarters - there are 100 coins in all - how many dimes?

I have been stuck on this problem for 30+ minutes and I can't seem to get the correct answer; there must be something that I am missing/doing wrong!! You own $19.75 in dimes and quarters There are ...
1
vote
1answer
54 views

Solving system of PDEs

I am stuck on the following problem: Solve for $f(x,y)$, where: $\frac{\partial f}{\partial y} = y$, $\frac{\partial f}{\partial x} = \frac{1}{2}xy$ My original strategy was to integrate the first ...
1
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0answers
49 views

Finding generators for a polynomial ideal given some polynomials belonging to it

Let $k$ be a finite field, $n$ a positive integer and $R := k[x_1,\ldots,x_n]$ the polynomial ring in $n$ variables. Let $f_1,\ldots,f_n\in R$ be polynomials with the following property: $f_i$ has ...
6
votes
5answers
836 views

Approximation to unsolvable system of equations

I am working on a project and need to find the "closest" numerical values that satisfy the following equations: \begin{equation} \left\{ \begin{array}{} A \cdot C = \frac{1}{2} \\ A ...
1
vote
1answer
47 views

Calculating the particular solution of the following nonhomogeneous system

The name of the game is systems of differential equations and matrix exponentials. I have the following problem: Apply the formula $\vec x(t) = e^{At} \vec c + e^{At} \int e^{At} \vec f(t) dt$ (where $...
2
votes
1answer
96 views

Solve a nonlinear system of coupled differential equations

I have this system of differential equations which describes the motion of a missile launcher model with 5 degrees of freedom: (1)$$(m_w +m_v +m_p)\ddot{y}_w - (m_v + m_p)h_v\ddot{\vartheta}_w \sin(\...
0
votes
1answer
21 views

Approximate a solution of a system of non linear equations

I have a system of non-linear equations of the form $$A x_1^B \exp \bigg(\frac{- C}{x_1} \bigg) = k_1$$ $$A x_2^B \exp \bigg(\frac{- C}{x_2} \bigg) = k_2$$ $$A x_3^B \exp \bigg(\frac{- C}{x_3} \bigg) ...
2
votes
1answer
33 views

System of two quadratic equations in two variables with two parameters leads to quintic polynomial

Actually, it's two closely related systems. Let $a,b \in \mathbb{Q}$ be the parameters. The first system has the form: $$(1+a y)x^2-2(a+y)x+(1+a y)=0 \\ (1-b x)y^2-2(b-x)y+(1-b x)=0$$ One of the ...
1
vote
1answer
39 views

Method for solving collection of simple PDEs

How would you go about evaluating the following collection of simple PDEs: $$\frac{\partial A_3}{\partial y} - \frac{\partial A_2}{\partial z} = yz$$ $$\frac{\partial A_1}{\partial z} - \frac{\...
0
votes
1answer
21 views

Second order system - find -3dB frequencies and magnitude response analytically

Let's take some simple second-order system like $H(s) = \frac{j\omega T}{(1+ j \omega T)^2} $. I know that the magnitude response is simply the absolute of the function and the -3dB frequencies can be ...
5
votes
4answers
92 views

Eliminate $\theta$

Eliminate $\theta$ in $$\sin \theta + \mbox{cosec} \, \theta = m$$ $$\sec \theta - \cos \theta = n$$ My approach- I multiplied the first equation by $\sin \theta$ and the second equation ...
0
votes
3answers
69 views

Find recurrence relation with general solution $a_n=A+Bn+C2^n+\frac{1}{3}n2^{n-1}$

General solution is: $a_n=A+Bn+C*2^n+\frac{n}{3}*2^{n-1}$ Can you give me some tips on solving this? Any help would be appreciated.
2
votes
3answers
58 views

Find $\lambda$ and $\theta$ such that it validates this matricial equation

Find $\lambda$ and $\theta$ such that it validates the matricial equation $$ \left( \begin{array}{cc} 1 & 2 \\ 2 & 3 \end{array} \right) % \left( \begin{array}{cc} \cos \theta \\ \sin \theta ...
0
votes
1answer
50 views

Find a least upper bound for $3^{x+y-4}+(x+y+1)2^{7-x-y}-3(x^2+y^2)$ with some constraint?

This is a question in vietnamese national math exam at the end of 12th grade. Given x,y are real numbers which satisfy the condition: $x+y+1=2(\sqrt{x-2}+\sqrt{y+3})$ Find a $m$ such that: ...
0
votes
0answers
15 views

Closed-form formula for system of two bivariate quadratic polynomials

Given a system of two bivariate quadratic polynomials: \begin{eqnarray} a_0 + a_1 x + a_2 y + a_3 xy+a_4 x^2 + a_5 y^2 &= 0 \\ b_0 + b_1 x + b_2 y + b_3 xy+b_4 x^2 + b_5 y^2 &= 0 \end{...
1
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3answers
54 views

Solve the system for the given parameter a

\begin{align} ax+y+z&=1,\\ 2x+2ay+2z&=3\\ x+y+az&=1 \end{align} I tried forming the system matrix and discuss it using its rank, but I'm not sure how to row reduce: $$\begin{pmatrix}a&...
2
votes
0answers
36 views

What is the difference between an autonomous system and a dynamical system?

Wikipedia says, Autonomous systems are closely related to dynamical systems. Any autonomous system can be transformed into a dynamical system and, using very weak assumptions, a dynamical system ...
0
votes
0answers
38 views

Solution to a non linear system of equations

Does there exist an interval I such that this system of equations has no solution? ...
-1
votes
2answers
52 views

Solve three equations for three unknowns. [duplicate]

So I have the following three equations which I do not know how to solve: -D * x - E * y = A + (R * D) E * F * x - D * F * y - G * z = B - (R * E * F) E * G * x - D * G * y + F * z = C - (R * E * G)...
2
votes
2answers
57 views

Value of $z$ in the given system of equations

If $$\{x\}+y+\lfloor{z}\rfloor=3.1$$ $$x+\lfloor{y}\rfloor+\{z\}=2.4$$ $$\lfloor{x}\rfloor+\{y\}+z=1.3$$ then find the value of $z$. My attempt: I converted fractional part of every equation to ...
0
votes
0answers
29 views

Workability of linear equation solving methods for different fields?

So far, I have mostly done linear algebra over $\mathbb R$ and $\mathbb{C}$. I know there exist very many methods to solve equation systems for those fields, of which a few are Gaussian Elimination, ...
0
votes
3answers
35 views

System of Equation

Solve the system of equations $$-x_1+x_2+x_3=a$$ $$x_1-x_2+x_3=b$$ $$x_1+x_2-x_3=c$$ I have tried writing the augmented matrix of the system of equations above and reducing it into echelon form ...
0
votes
0answers
11 views

An algorithm to find the general classical solution to a linear gradient system in partial derivatives

I'm looking for a book where the algorithm to construct the general solution for system $$\nabla u(x,y) = \vec a(x,y)\cdot \nabla v(x,y)$$ is given. Could ypu please advice me some source?
0
votes
2answers
82 views

Why can the equation Ax = b not be solved for every b

Let $A$ be a $3 \times 2$ matrix . Explain why the equation $A\vec{x} = \vec{b}$ cannot be solved for every $\vec{b}$ in $\mathbb{R}^3$. What about a $4 \times 3$ matrix? I'm not sure how to answer ...
0
votes
0answers
30 views

Solving a system of N-1 Ist order ODEs by Euler's Method

In order to solve a system of N-1 first order ODEs by Euler's Method For N = 4; t=0, h= 0.1, x= 0.1 should the Euler formula be? $U_n(t+h) = U_n(t) + h F_n(x_n, t_n)$ for n = 1, 2,..,N-1 but we ...
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votes
2answers
44 views

What can be a good programming algorithm to solve the given equation other than the brute force? [closed]

Find all $x$, $y$ and $z$ for $n=100$; $$x^2 + y^2 + z^2 = n$$ $x,\ y,$ and $z$ should be positive integers.
0
votes
2answers
24 views

Simultaneous recurrence relations

Currently working on solving this set of three simultaneous recurrences, but having some trouble. Tried various substitutions, but still cannot seem to make any progress. Also, none of the three ...
7
votes
3answers
159 views

A System of Infinite Linear Equations

Suppose that $\{a_{i}\}_{i=-\infty}^{\infty}$ with $\sum_{i=-\infty}^\infty a_{i} \lt \infty$ is known and that $\{b_i\}_{i=-\infty}^{\infty}$ is such that $$\sum_{i=-\infty}^\infty a_{i}b_{-i} =1,$$ ...
1
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4answers
47 views

Symmetric system of $3$ equations

I need help solving the following system for all real ordered triples $(x,y,z)$ without guessing and checking: $$x+y+z=23$$ $$xy+yz+xz=144$$ $$xyz=252$$ Preferably, the solution should use methods ...
3
votes
1answer
48 views

Solving a system of non linear equations

I have got a system of non-linear equations of the form $$A x_1^B \exp \bigg(\frac{- C}{x_1} \bigg) = k_1$$ $$A x_2^B \exp \bigg(\frac{- C}{x_2} \bigg) = k_2$$ $$A x_3^B \exp \bigg(\frac{- C}{x_3} \...
1
vote
1answer
38 views

System of two Nonlinear equations

I have a probably very simple problem here. A system of nonlinear equations. $$\left\{ \begin{align} & {{x}^{2}}+{{y}^{2}}=26 \\ & x+{{y}^{2}}=6 \\ \end{align} \right.$$ I started with ...
0
votes
0answers
41 views

Incorrect answer - Simultaneous Differential Equations

The questions states solve for y such that $$y' = \begin{bmatrix} -4 & 2 & 1 \\ 1 & -3 & 1 \\ 3 & -3 & -2 \\ \end{bmatrix}y , y(0)= c = \begin{bmatrix} 1\\5\\3 \end{...
1
vote
2answers
23 views

Dimension of the span of two parallel lines in $R^4$.

I am asked if the following question is true or false: Let $r,s$ be two parallel lines in $R^4$ then the dimension of $Span(r \cup s)$ is strictly less than $3$. I think this is true because two ...
2
votes
4answers
111 views

Solution of $(n+1)^{1/3}-n^{1/3}=\frac{1}{12}$

Solve the given equation for $n$ $(n+1)^{1/3}-n^{1/3}=\frac{1}{12}$ How to approach this particular question? Sorry cannot show any work because the only approach I can see is take cube on both ...
3
votes
1answer
74 views

Help required in finding solution to overdetermined system of equations?

I have access to M probability measures, $P_e(c_1),P_e(c_2),\cdots,P_e(c_M)$, defined as \begin{equation} P_e(x) = p(x|y) = p(y|x)\cdot \mathbb{P}(X=x) \frac{1}{\sqrt{2\pi\sigma^2}} \exp\Big[-\frac{(y-...
1
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2answers
31 views

matrix calculation

Let $p= \begin{pmatrix} x & y \\ z & v \end{pmatrix}\in M_2(\mathbb{C})$ such that $p^2=\overline{p}^t=p$ and rank(p)=1. Why is $p=\begin{pmatrix} t & l\sqrt{t(1-t)} \\ \overline{l}\sqrt{...
2
votes
4answers
113 views

Is this possible to solve through algebra?

$$150 \equiv 17 \mod x, \qquad 100 \equiv 5 \mod x $$ Solve the simultaneous equation? Is this even a simultaneous equation? How do I find the value of $x$ too? I was doing a question and came up ...
3
votes
3answers
52 views

If $a-c = 9$ then find the value of $b-d$.

If $a,b,c,d$ are positive integers such that $\log_a b=\frac{3}{2}$ and $\log_c d=\frac{5}{4}$, if $a-c = 9$ then find the value of $b-d$. We get $b=a^{3/2}$ and $d=c^{5/4}$ Hence $b-d=a^{3/2}-c^{...
1
vote
1answer
30 views

Linearly independent subset - a simple solution?

Problem: Let $\{ v_1, \ldots, v_n \}$ be a linearly independent subset of $V$, a vector space. let $$ v= t_1 v_1 + \cdots + t_n v_n $$ where $t_1, \ldots t_n \in \mathbb{R}$. For which $v$ is ...
0
votes
1answer
30 views

Solve Graphically

Solve the given systems of equations by graphical method: $$x^2+y^2=5$$ and $$y=2x$$ My Attempt Let's have a look at the second equation ; $$y=2x$$ This is a linear equation in two variables ...