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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-1
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1answer
57 views

Unordered pairs solution

Please help me with this question.$$$$ How many unordered triplets $(x,y,z)$ , subject to constraints, $(x^4-2x^3)_{cyclic}\leq0$ , satisfy the system of equations: ...
7
votes
1answer
190 views

Prove or Disprove the Existence of Solutions…[linear algebra] - a C.S.I.R Question

Let $A$ be a $3\times 4$ and $b$ be a $3\times 1$ matrix with integer entries.Suppose that the system $Ax=b$ has a complex solution. Then which of the following are true? 1)$Ax=b$ has an integer ...
1
vote
1answer
64 views

how to work out 3 equations simultaneously

So i was doing this linear programming question and got stuck on this part, so how do you workout simultaneously $2x + 3y = 30 $ $(2/3)x + 2y = 16 $ $(16/3)x + 4y = 64$ According to lpsolve we ...
1
vote
2answers
88 views

I have the Eigenvalues, how do I get Eigenvectors?

My matrix is \begin{array}{ccc} 3 & 4 & 5 \\ -2 & 7 & 3 \\ 5 & -8 & -3 \end{array} Through the rule of Sarrus, I know (approximately) $\lambda_1 = 5.9$ $\lambda_2 = 3.5$ ...
6
votes
2answers
63 views

How to solve this nonstandard system of equations?

How to solve this system of equations $$\begin{cases} 2x^2+y^2=1,\\ x^2 + y \sqrt{1-x^2}=1+(1-y)\sqrt{x}. \end{cases}$$ I see $(0,1)$ is a root.
1
vote
0answers
31 views

Expressing the Solution to a System of Differential Equations

My professor wrote the solution to a system as $$X = C_1 \begin{bmatrix}1 \\2 \end{bmatrix} e^{\lambda_1t} + C_2 \begin{bmatrix}3 \\4 \end{bmatrix} e^{\lambda_2t}$$ Where the column vectors are the ...
0
votes
1answer
32 views

Find $a$ and $b$ in a 4 equation system

$a, b \in\mathbb{R}$. I have four equations: $$x+3y-2z+t=-3$$ $$3x+11y+az+5t=2$$ $$3x+12y-6z+6t=b$$ $$4x+15y-8z+8t=-5$$ I have to find out the values of $a$ and $b$ where the system is solvable (has ...
0
votes
3answers
44 views

Solving Linear System with inequalities

I have the following system: \begin{align} b - x = 0 \\ a - 0.33b - 0.5x =0 \\ d - 0.33b = 0 \\ a - 0.33b + c = 0 \\ a + b + c + d + 2x = 1 \\ a + b + c + d - 8.8x \le 0 \\ a + b + c + d - 7.27x ...
1
vote
0answers
33 views

Converting second order system into first order system (ODE)

The second order equation $\frac{d^2\vec{x}}{dt^2} = A\vec{x}\ + \vec{g}(t)$ models an earthquake's effect on a 7-story building. Let $x_j(t)$ be the displacement of the $j$th floor with respect to ...
1
vote
0answers
25 views

Solving a linear system in function of a parameter

Problem: Solve the following system in function of the parameter $b$: \begin{align*} \begin{cases} -bx + 2y - (2+b^2)z + bu &= -2 \\ x -2y + bz -u &= 0 \\ x + (2b-4)y + (2-b)z + (b-1)u &= ...
-1
votes
2answers
28 views

Converting a second order n x n system into a first order 2n x 2n system

Say I have the following second order 7 x 7 system of equations: $x_1'' = 10(x_2- x_1- 1)$ $x_2'' = 10(x_3- 2x_2+ x_1)$ $x_3'' = 10(x_4- 2x_3+ x_2)$ $x_4'' = 10(x_5- 2x_4+ x_3)$ $x_5'' = 10(x_6- ...
0
votes
0answers
39 views

Solving a general system of linear equations

We are given a system with n linear equation: $$\forall i\in \{1,...,n\}: i \cdot x_i + \sum_{j=i+1}^{n}x_j= \frac{i}{n}$$ Prove that the solution for this system of equation is $$\forall i\in ...
4
votes
1answer
104 views

How to determine when this two variable transformation is invertible?

I am given: $$ X= U \cos(V) \tag{1}\\ $$ $$ Y = U \sin V \tag{2}$$ Now, I need to: a) Give the respective ranges for $U$ and $V$ in order that the transformation defined is one to one. and ...
-1
votes
1answer
41 views

Algebra - Solutions of linear systems

How would I find the real values of $k$ such that the following linear system does not have a unique solution? $$\begin{cases} x + 3y + kz = a \\ 2x + (2k+2)y + (3k-2)z = b \\ kx + (k+4)y + 4z = c ...
0
votes
1answer
46 views

The Lotka-Volterra Model Continued

Consider the following system of equations, and assume that population of prey is measured in thousands, and that the population of predators is measured in hundreds. $$\frac{dx}{dt} = ...
0
votes
1answer
88 views

Predator Prey Model [closed]

Consider the following system of equations, and assume that population of prey is measured in thousands, and that the population of predators is measured in hundreds. $$\frac{dx}{dt} = ...
0
votes
1answer
39 views

Solve system of trigonometric equations

How would you solve a system like this $$ \left\{ \begin{aligned} 0&=E-\sin\left(\theta_1\right) + K \sin\left(\theta_2 - \theta_1\right)\\ 0&=E+\sin\left(\theta_2\right) - K ...
1
vote
4answers
63 views

Why would I divide these two equations to solve for i?

I have the following two equations representing a longer actuarial practice question. I properly set up the equations, but am stumped on how to solve them. The book says to divide the first by the ...
3
votes
2answers
48 views

How to solve the equations of linear combination of sigmoid functions?

Let $\sigma(x)=\frac{1}{1+e^{-x}}$ be the sigmoid function. How to solve such kind of equations? \begin{align*} \sigma(x+y)+\sigma(x-y)=a\\ \sigma(2x+y)+3\sigma(3x-y)=b\\ \end{align*} I guess this ...
0
votes
1answer
50 views

Non computational approach to this equation?

I was thinking about the following problem (not homework): Let $a,b,c,d \in {0,1,2,3,4,5,6,7,8,9}$ Find all four digit numbers $abcd$ where the two digit numbers $$ ...
0
votes
1answer
24 views

Solving the equations .

Say , I have two equations : $$y_1=a+bx_{1}+e_1$$ $$y_2=a+bx_{2}+e_2$$ Say , $a=.5$ , $b=2.1$ , $x_1=2$ , $x_2=2.2$ . Now if $e_1=e_2$ , I have to find the relationship between $y_1$ and $y_2$ . ...
0
votes
1answer
88 views

Are there any system(s) of mathematics whose relationship between variables bears difference to that found within mainstream mathematics?

I have been reading up on boolean algebra quite recently, for those not familiar, this type of mathematical system has much to do with the way logic is represented (and is primarily applied to, though ...
0
votes
1answer
30 views

Solving a system of equations containing complex numbers - Gaussian elimination

Problem: Determine the solutions in $\mathbb{C}^3$ of the following system over $\mathbb{C}$: \begin{align*} \begin{cases} 2x+iy-(1+i)z &=1 \\ x-2y+ iz &= 0 \\ -ix +y -(2-i)z &= 1 ...
0
votes
1answer
10 views

Different results while calculating eigenvectors with Gaussian elemination

Regarding this matrix $\begin{matrix} 1 & 1 \\ 1 &-1 \\ \end{matrix}$. In the end I have to solve this equation system: $(\sqrt2-1)x_1-x_2=0$ $-x_1+(\sqrt2+1)x_2=0$ While the ...
1
vote
0answers
59 views

Does this linear system of 5 unknowns and 2 equations have multiple solutions?

\begin{cases} x+ 2y - z + w - t = 0 \\ x - y + z + 3w - 2t = 0 \end{cases} Add 1st to the 2nd: $$2x + y + 4w - 3t = 0 \\ y = -2x - 4w + 3t = 0$$ Substitute y in the 1st: $$x - 4x - 8w + 6t - z ...
1
vote
1answer
39 views

How to describe behavior of population system, given by system of ODEs?

So I have a system of equations:$$x'(t)=x(t)(4-2x(t)-y(t))\\y'(t)=y(t)(3-x(t)-y(t)) $$ What I understand so far is: if we have x being the population of prey and y is the population of predators. x ...
9
votes
2answers
123 views

How to prove the cubic formula without root extraction

I'm trying to prove the cubic formula, in the following form: Given a field $F$ and $x,p,q\in F$, define $m=\frac p3$ and $n=\frac q2$, and suppose also that $\gamma,\tau$ are given such that ...
1
vote
1answer
25 views

Why do the 1's in Gauss Jordan RREF need to be along main diagonal and not other diagonal?

I've practiced G-J elimination and understand most of the algorithm insofar as it represents the different manipulations one can apply to a system of equations. However, when we're talking about ...
-2
votes
1answer
41 views

Trouble with two equations with 4 unknowns [closed]

I was wondering if I could receive assistance for the following system: $$\begin{cases}(x/a)^{3.2}+(y/b)^{3.2}=1\\ a/b = 174.1/86\end{cases}$$ I'm looking for integer solutions or how to find them ...
2
votes
0answers
19 views

Function intersecting 3 points & deriviate is positive for a range of x values

Thank you for taking the time to help out on this question. I'm looking for a function that intersects 3 points, and a derivative for every value of x between x=0 and x = 365 where dy/dx >= 0. My ...
0
votes
0answers
19 views

System of equations and chain rule

I have this system $\nabla b(z_1,\ldots,z_m)=\psi^\prime(\theta)\nabla\theta(z_1,\ldots,z_m)$. Where we have $\theta(z_1,\ldots,z_m)=\sum_i^m z_i$ and $b(z_1,\ldots,z_m)$=$\sum_i^m z_i^2$ What is ...
0
votes
1answer
20 views

Discrete convolution equation

Let $x_1 = (x_1^k)_{k =-\infty}^{+\infty}$, $x_2 = (x_2^k)_{k=-\infty}^{+\infty}$, $x_3 = (x_3^k)_{k=-\infty}^{+\infty}$ be three sequences of real numbers such that $x_j^k = 0$ for $k < -m_j < ...
1
vote
1answer
47 views

Is it possible to solve this system of equations? [duplicate]

Consider a system of equations given below: $ p_1 + p_2 + p_3 + p_4 + p_5 = 1 $ $ x_1*p_1 + x_2*p_2 + x_3*p_3 +x_4*p_4 =0$ $ x_1^2*p_1 + x_2^2*p_2 + x_3^2*p_3 +x_4^2*p_4 =1$ $ x_1^3*p_1 + ...
0
votes
1answer
29 views

tridiagonal matrix with a corner entry from upper diagonal

I am trying a construct a matlab code such that it will solve an almost tridiagonal matrix. The input I want to put in is the main diagonal (a), the upper diagonal (b) and the lower diagonal and the ...
0
votes
2answers
28 views

Is it possible to have a system of equations that all equal 0, and not have each unknown's value be 0?

I'm doing about a 2 hour long homework assignment where by hand I must construct a 10x10 matrix representing a system of equations. Based on the pattern I'm seeing, I can tell all of the equations ...
10
votes
1answer
299 views

How prove this systems-equation has least two postive integers solution

Show that: for any $k\ge 100,(k\in N^{+})$, there exsit $p\in N^{+}$, such $$\begin{cases} a+b+c=k\\ abc=p\\ a>b>c \end{cases}$$ has at least two postive integers solution $(a,b,c)$ ...
1
vote
2answers
39 views

Solving simultaneous PDEs

Given the equations (1):$$\frac{\partial u}{\partial t}+g\frac{\partial \eta}{\partial x}=0$$ and (2):$$\frac{\partial\eta}{\partial t}+H\frac{\partial u}{\partial x}=0$$ can we combine the two ...
0
votes
1answer
25 views

Matrix with given row and column sums

Let $N$ and $K$ be two given integer numbers different from zero. Let $S_n$ with $n=1,...,N$ and $C_k$ with $k=1,...,K$ strictly positive integer numbers such that $$ ...
2
votes
4answers
59 views

Simultaneous Quadratic Equations: $x^2 + y ^ 2 - 2 x + 6y - 35 = 0$ and $2x + 3y = 5$

I've been given the task to simultaneously solve: $$x^2 + y ^ 2 - 2 x + 6y - 35 = 0$$ $$2x + 3y = 5$$ I've tried applying the substitution method by reordering the second equation to both $x$ and ...
1
vote
1answer
24 views

Solution of system of equations in prime fields

In 'Algebra', Artin writes that the system of equation: $$8x+3y = 3$$ $$2x+6y = -1$$ have no solutions in $\mathbb{F}_2$ and $\mathbb{F}_3$ as the determinant (of the coefficient matrix) evaluates ...
1
vote
1answer
39 views

System of ODEs obtained by using the method of characteristics for $u_x + 2u_t - 4u = e^{x+t}$

I have a question which requires me to use the method of characteristics in order to solve the PDE $u_x + 2u_t - 4u = e^{x+t}$. This results in the system of ODE's $\frac{dx}{dr} = 1 , \frac{dt}{dr} ...
0
votes
1answer
104 views

Solve the system $ x \lfloor y \rfloor = 7 $ and $ y \lfloor x \rfloor = 8 $.

Solve the following system for $ x,y \in \mathbb{R} $: \begin{align} x \lfloor y \rfloor & = 7, \\ y \lfloor x \rfloor & = 8. \end{align} It could be reducing to one variable, but it is ...
0
votes
2answers
37 views

Simple trigonometrical equations

I'm having difficulties in solving the simultaneous equations $$ \begin{cases} \sin(x+y)=\frac{1}{\sqrt{2}}\\ \cos(2x+y)=\frac12 \end{cases} $$ for $0^{\circ}\le x,y\le 90^{\circ}$. The answer is ...
1
vote
2answers
78 views

Analog clock with same hands - sometimes one can't tell time [duplicate]

There is an accurate analog clock, however both hands are the same size and shape. How many moments during a day a person can not conclude current time from the position of the hands? This is from a ...
0
votes
1answer
15 views

Differential system, a matrix with eigenvalue

Let's say that we have $n$ differential equations written in the form: $x'(t) = Ax(t) + v \exp(\lambda t)$, where $v$ is the eigenvector of $A$ such that $A v = \lambda v$ and $A$ is a $n \times n$ ...
0
votes
2answers
32 views

Can the following system be solved symbolically/analytically?

I have the following system of equations with variables $a,m$, and I'm wondering—can this system be solved symbolically/analytically? \begin{align} m &= 100 + \frac{ \left( 200 ...
2
votes
0answers
54 views

How to find whole number answers in systems of square root equations

Given the following 4 equations, can you find 4 whole number answers using whole number variable inputs? $x,y,z$ where $x>y>z$ $Eq 1 = (x^2-2xy+y^2-2xz+z^2)^{\frac{1}{2}} $ $Eq 2 = ...
0
votes
0answers
24 views

How do I solve massive system of equations (with lots of variables) quickly?

Just wondering how to solve system of equations involving 3+ unknowns quickly. In my math class, we're given questions like these which involve solving huge system of equations on a time limit, ...
0
votes
2answers
39 views

Find $x(t)$ and $y(t)$ which satisfy the following differential equations

Find $x(t)$ and $y(t)$ which satisfy $3\dot x + \dot y +5x-y=2e^{-t}+4e^{-3t}$, $\dot x + 4\dot y -2x+7y=-3e^{-t}+5e^{-3t}$, subject to $x=y=0$ at $t=0$. This is how I tried it: If we multiply ...
1
vote
2answers
167 views

$10$ Equations in $10$ variables

Define, $$F_k = xp^k + yq^k + zr^k + us^k + vt^k$$ Let, $$F_0 = 2$$ $$F_1 = 3$$ $$F_2 = 16$$ $$F_3 = 31$$ $$F_4 = 103$$ $$F_5 = 235$$ $$F_6 = 674$$ $$F_7 = \color{blue}{1667}$$ $$F_8 = ...