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
37 views

gaussian elimination to solve a question (using a paramter)

I want to solve : x2+x3=0 -x1 -x3=0 x1-x2 =0 I got the $x_1 = -t, x_2=-t, x_3=t$. But the book has $x_1 = t, x2=t, x3=-t$. ...
0
votes
2answers
29 views

Find system of equations such that

Find system of equations that will describe: a) plane $M \subset \mathbb{R}^3$ passing through the points $(6,1,-3), (1,5,1), (1,8,2)$ b) line $L \subset \mathbb{R}^3$ passing through $(1,2,-1), ...
1
vote
2answers
100 views

Solving a non-linear, multivariable system of equations

I'm researching the mathematics behind GPS, and at the moment I'm trying to get my head around how to solve the following system of equations: $\sqrt{(x-x_1)^2+(y-y_1)^2+(z-z_1)^2}=r_1$ ...
0
votes
1answer
52 views

Solving 4 unknowns with 4 equations all equal to zero

I have the following equations: $$\begin{align} a&=0.35a+0.35d\\ b&=0.65a+0.65d\\ c&=0.35b+0.35c\\ d&=0.65b+0.65c \end{align}$$ I know $b=d$, but where do I go from here? I have a ...
0
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2answers
53 views

Solve 5 unknowns with 5 equations

I have the following set of equations: $A = x_1x_2x_3x_4x_5$ $B = x_1x_3x_5 + x_1x_4x_5 + x_2x_4x_5 + x_2x_3x_4$ $C = x_3 + x_4 + x_5$ $D = x_1x_2x_3x_4$ $E = x_1x_3 + x_1x_4+x_2x_4$ Where A, B, ...
0
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1answer
63 views

How to solve the system of 4 equations of four unknowns

Solve this system of the four equations of four unknowns $a, b, c, d>0 $ $$ 165(a+b+c)=abc\tag1 $$ $$220(a+b+d)=abd \tag2 $$ $$297(a+c+d)=acd\tag3 $$ $$540(b+c+d)=bcd \tag4 $$ I tried to ...
3
votes
2answers
36 views

How to solve the given system of equations for $I_1, I_2, I_3$?

I have this system of equations: \begin{cases} I_1 = I_2 + I_3 \\ \epsilon_1 - I_1(R_1 + R_2) - I_2 R_3 = 0 \\ \epsilon_1 - I_1(R_1 + R_2) - I_3(R_4 + R_5) + \epsilon_2 = 0 \end{cases} I want to solve ...
0
votes
0answers
40 views

A simple non-linear equation.

Let ${\rm a}$ and ${\rm b}$ be two given vectors in ${\mathbb R}^n$. Find ${\rm u}\in {\mathbb R}^n$ and $x\in[0,\infty)$ such that $$ {\rm a} +{\rm b}x+\frac{1}{2}x^2{\rm u}=0, \quad \|{\rm u}\|=1 ...
0
votes
0answers
33 views

How can I find multiple solutions for a system of equations?

I'm writing a program for CheckIO.org that is supposed to return an array, $$ \begin{bmatrix} x\\ y\\ z \end {bmatrix} $$ , that satisfies the System of Equations $$ A \begin{bmatrix} x\\ y\\ z \end ...
2
votes
0answers
21 views

Solve Intergal Equation of form g.u1=Int(K.u2) for u1 and u2

I'm trying to find a solution to a differential equation of an unusual form: $$g(x) u_1(x)=\int_a^b K(x,y) u_2(y) dy$$ where $g(x)$ and $K(x,y)$ are known and $u_1(x)$ and $u_2(x)$ are complex ...
1
vote
1answer
36 views

Find integral of the 2 by 2 system of ODE

We want to find a function $F(x(t),y(t))=c$ where $x(t),y(t)$ are solutions to the system $\begin{bmatrix} \dot x=\frac{t-y}{y-x} \\\dot y=\frac{x-t}{y-x}\end{bmatrix}$. Such a function $F(x(t),y(t))$ ...
2
votes
1answer
24 views

Add together simple equations

I have three equations $$ x = 20 \\ -x+a = 10 \\ y = 2 $$ Can I add these equations and get $$ x-x+a+y = 20+10+2 \\ a+y = 32? $$ If yes, what is the name of the rule applied?
2
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0answers
20 views

Solving equation set with boolean operators and very specific format

I have to write a program to solve a set of equations like the following (+ is XOR and * is ...
0
votes
0answers
14 views

Show the following system is not possible

Assume throughout that the base field is the prime field $\mathbb{F}_2$. I have two $n \times n$ matrices: $I_n$, the $n \times n$ identity matrix, and $C_n$ the matrix obtained from $I_n$ by shifting ...
0
votes
1answer
30 views

System of homogeneous linear equations issue

Solve the following system: $4x-12y+z=0\\ x-5y-z=0\\ -4x+12y+z=0$ So in matrix form it is $ \left(\begin {matrix} 4 & -12 & 1 \\ 1 & -5 & -1 \\ -4 ...
1
vote
1answer
23 views

Find base vectors and dim

Find base vectors and dim of a space described by the following system of equation: $$2x_1-x_2+x_3-x_4=0 \\ x_1+2x_2+x_3+2x_4=0 \\ 3x_1+x_2+2x_3+x_4=0$$ I did rref of the matrix and as a result i get: ...
1
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1answer
45 views

How can I solve the following exercise

How can I solve the following exercise $$φ_1(x)=e^x-\int_{0}^{x}φ_1(t)dt+4\int_{0}^{x}e^{x-t}φ_2(t)dt$$ $$φ_2(x)=1-\int_{0}^{x}e^{-x+t}φ_1(t)dt+\int_{0}^{x}φ_2(t)dt$$
0
votes
0answers
32 views

What are “symmetry arguments” in the context of solving systems of equations?

What and how are the "symmetry arguments" used to solve a system of equations? My text makes extensive use of this argument but do not provide and explanation of how it works or the definition of ...
0
votes
1answer
26 views

Solve $|x - z_1| = d_1 + y$ and $|x - z_2| = d_2 + y$ simultaneously for $x$ and $y$

Given the two equations $|x - z_1| = d_1 + y$ and $|x - z_2| = d_2 + y$ , and suppose that $z_1, z_2 \in \mathbb{R}$, $z_1 \neq z_2$ and $d_1, d_2, \in \mathbb{R}_{> 0}$ are all known reals, solve ...
2
votes
1answer
42 views

System of equations, 3 equations and 3 unknown

I have a system of equations that I'm trying to solve, $Mb = x$ $M=\begin{bmatrix} e^z &e^z &e^z \\ aX_1 &bX_1 &cX_1 \\ aX_2 &bX_2 &cX_2 \end{bmatrix}$ $b = ...
0
votes
1answer
41 views

Gauss' method to solve the following system of equations

I need to use Gauss' method to solve the following system of equations and to describe its solution set. Can anyone help me getting started. \begin{alignat*}{8} x & + & y & + & z ...
-1
votes
2answers
41 views

Solve three simultaneous equations with 3 unknowns

(b) An electrical circuit comprises three closed loops giving the following equations for the currents $i_1, i_2$ and $i_3$ \begin{align*} i_1 + 8i_2 + 3i_3 &= -31\\ 3i_1 - 2i_2 + i_3 ...
-1
votes
1answer
61 views

Does $x^2=83\pmod{101}$ have solutions? without calculating them

Does $x^2=83\pmod{101}$ have solutions? without calculating them. I'm not sure how to tackle this without solving, I tried using chinese remainder and quadratic reciprocity.
0
votes
2answers
80 views

Solve a differential equation system

I am solving a physics problem and done almost everything to a couple of last steps. I currently have two differential equations which I need to solve for functions$x(t)$ and $y(t)$: $$ \ddot x =\dot ...
1
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0answers
32 views

Solutions to linear equations

Am I right in thinking that the following augmented matrix equation only has one solution: $\begin{bmatrix} 0 & 1 & 0 & 4\\ 0 & 0 & 1 & 10 \end{bmatrix} $ i.e., if the ...
1
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0answers
130 views

Linear Algebra Proof for matrices

Could someone possibly help me in proving this: Let $A$ be the augmented $m \times (n + 1)$ matrix of a system of m linear equations with $n$ unknowns. Let $B$ be the $m \times n$ matrix obtained ...
0
votes
1answer
47 views

Who to solve this linear modular equation system?

I have this equation system: a + b + c (mod 11) = 8 9a + 3b + c (mod 11) = 2 16a + 4b + c (mod 11) = 9 Unfortunately I totally don't know how to solve it. It is in general part of Lagrange's ...
2
votes
3answers
67 views

Solving $n$ unknowns with $n$ independent equations

Is it always possible to solve $n$ independent equations with $n$ unknowns? Or is it possible to solve the following 3 equations with 3 unknowns? $$x + y + z = a$$ $$x^2 + y^2 + z^2 = b$$ $$x^3 + ...
0
votes
0answers
9 views

System of one-dimensional PDES

I've just started an introductory course in PDEs, but am having a lot of trouble knowing how to approach some problems. In the problem I am working on, we have the functions $\rho'(x, t)$, $\mu'(x, ...
0
votes
0answers
18 views

Question about DE related to physics; includes Hooke's Law and Newton's Second Law as well as system of DE equations and solutions, and a phase plane.

I mainly need help with part A, and a little bit on B and C. Thank you in advance for your answer or any comment or edit that helps!!! A second-order DE can be sometimes solved with clever ...
0
votes
1answer
26 views

System of linear inequalities

Consider the following system of inequalities. $$x_1 − x_2 ≤ 3\\ x_2 − x_3 ≤ −2,\\ x_3 − x_4 ≤ 10,\\ x_4 − x_2 ≤ α,\\ x_4 − x_3 ≤ −4,$$ where $\alpha$ is a real number. A value for $\alpha$ for which ...
1
vote
0answers
77 views

Can I find a closed form solution for this system of equation?

I'm trying to find a closed form solution $(x_0,y_0,v_x,v_y)$ for the following equation, where $a$ and M(t) are known numerically. $$ ...
1
vote
2answers
17 views

How to get an expression for $\frac{e1}r$ out of these four equations?

Given the following equations: $$y = g_2 \cdot e_3 \\ e_3 = e_2 - y \cdot h_2 \\ e_2 = g_1 \cdot e_1 \\ e_1 = r - h_1 \cdot e_2 - h_3 \cdot y$$ How can I get an expression of $\dfrac{e1}r$ in terms ...
0
votes
1answer
30 views

Find the matrix A in the following

$$\left[ \begin{array}{cc} 2 & -6&-4 \\ -2 & 7& 3 \\ 3&-8&-6 \end{array} \right]^{-1} +2 \cdot A= \left[ \begin{array}{cc} 7 & 2&5 \\ 6 & -10& -7 \\ ...
0
votes
0answers
15 views

Determining the solution of a closed loop system

Then applying this to our system, we get $u(t)=-2(q'(t)+\epsilon\sin{(\omega t)})-(q(t)+\epsilon\sin{(\omega t)})$ I want to determine the solution of this closed loop system and that the ...
5
votes
1answer
127 views

Convergence of Conjugate Gradient Method for Positive Semi-Definite Matrix

Let $A\in\mathbb{R}^{N\times N}$ be a positive semi-definite matrix, given $b\in\mbox{Col}\left(A\right)$ we want to solve the equation system $Ax=b$ . To add some notation, we define ...
0
votes
1answer
40 views

The system of Diophantine equations.

Often seen similar systems of equations. Usually consider such systems in which decisions no. Such as there. Is there $a,b,c,d\in \mathbb N$ so that $a^2+b^2=c^2$, $b^2+c^2=d^2$? I think it would be ...
1
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2answers
41 views

Number of solutions of a variable matrix

Given matrix: $$\left(\begin{array}{ccc|c} c & c & 1-c & 1\\ c & c^{2} & 1-c^{2} & 1\\ 2c & c+c^{2} & 2-2c & c+2 \end{array}\right)$$ row reduced to: ...
0
votes
3answers
61 views

Why does <strike>$(2^2\cdot 3^3)^2 = (2^2\cdot 3^3\cdot 4^4$)</strike>? nevermind, my bad [closed]

I was messing around and I noticed that $(2^2\cdot3^3)^2 = 2^2\cdot 3^3\cdot 4^4$. May sound strange but $108$ is a mystical number of ancient India, and was trying to deduce why, when I noticed it ...
0
votes
2answers
43 views

$ f(x) = -\ln\left(\tanh\frac{x}{2}\right) = \ln \frac{e^{x}+1}{e^{x}-1} $ prove $f(x) = f^{-1}(x)$

$$ f(x) = -\ln\left(\tanh\frac{x}{2}\right) = \ln \frac{e^{x}+1}{e^{x}-1} $$ Prove $f(x) = f^{-1}(x)$ when $x\gt 0$. I tried to do $f^{-1}(x) = \dfrac 1 {f(x)}$. Can you help me ?
2
votes
3answers
74 views

Problem for system of equations

Find the solution of the following set of equations \begin{equation} \begin{cases} yz-2z+x-1=0 \nonumber \\ zx+y-z-2=0 \nonumber \\ xy-2x-y+z+2=0 \end{cases} \end{equation}
2
votes
1answer
107 views

Determine the value of k for which a matrix system is consistent and the values for which it is inconsistent

The non-homogenous system is as follows: $$3x+2y+5z=10\\ 3x-2y=7\\ 6x+4y-10z=k$$ I have determined that: $$z=1-\frac{k}{20}\\ y=\frac{k}{16}-\frac{1}{2}\\ x=2+\frac{k}{24}$$ What are the values of ...
2
votes
1answer
25 views

Solving a homogenous system of equations

$x_1 - x_2 - 2x_3 + x_4 = 0 \\ -3x_1 + 3x_2 + x_3 - x_4 = 0 \\ 2x_1 - 2x_2 + x_3 = 0$ How do I solve this system of equations? I know this is a homogenous system. By applying elementary row ...
0
votes
1answer
65 views

Separation of Variables vs Fourier Transform (for PDE)

I would like to know how can I know if I have to solve a PDE (Heat Equation, Laplace Equation, Wave Equation, etc.) using Separation of Variables or Fourier Transform. Which boundary conditions do I ...
0
votes
0answers
50 views

Solving infinite system of polynomial equations with equal powers

I have the following infinite system with unknown $\{\mu_i\}_{i=1}^k$, $$ \mu_1^{\ell} a_1(\ell) + \mu_2^{\ell} a_2(\ell) + \ldots + \mu_k^{\ell} a_k(\ell) = b(\ell), $$ for $\ell \in ...
30
votes
5answers
2k views

System of 4 tedious nonlinear equations: $ (a+k)(b+k)(c+k)(d+k) = $ constant for $1 \le k \le 4$

It is given that $$(a+1)(b+1)(c+1)(d+1)=15$$$$(a+2)(b+2)(c+2)(d+2)=45$$$$(a+3)(b+3)(c+3)(d+3)=133$$$$(a+4)(b+4)(c+4)(d+4)=339$$ How do I find the value of $(a+5)(b+5)(c+5)(d+5)$. I could think only of ...
1
vote
1answer
18 views

Finding the equation to the variables with imaginary numbers

The numbers are $2, -i, i$. The answer is $x^3 - 2x^2 + x - 2 = 0$. But I have no earthly idea how to get from the answer to the problem with imaginary numbers.
4
votes
4answers
246 views

Solve a system of equations of ten unknowns.

I have the following problem: Find all $a_1,a_2,a_3,....,a_{10} \in\{1,2,3,...,10\}$ satisfying $\hspace{2cm}\begin{align} a_1+a_2+a_3 &=k\\ a_3+a_4+a_5 &=k\\ a_5+a_6+a_7 &=k\\ ...
0
votes
2answers
41 views

How to solve this system without WolframAlpha

How can I solve this system without using WolframAlpha or any other program? $$\begin{equation} \begin{cases} 2x_1+\lambda x_2+3x_3+4x_4=1\\x_1-x_2+9x_3+7x_4=3\\3x_1+5x_2+\lambda ...
0
votes
1answer
33 views

nontrivial solutions in matrix

Determine if the system has a nontrivial solution. $-3x_1+4x_2-8x_3=0 $ $-2x_1+5x_2+4x_3=0 $ I know that in order to find if a system has nontrivial solutions, all on the entries in a matrix row ...