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Questions tagged [systems-of-equations]

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.

2
votes
2answers
26 views

True or false statements about a square matrix

Consider the following four statements about an $n \times n$ matrix $A$. $(i)$ If $det(A) \neq 0$, then $A$ is a product of elementary matrices. $(ii)$ The equation $Ax=b$ can be solved ...
0
votes
2answers
16 views

How to find a,b and c in terms of the semi perimeter (s) from this equation?

I have an equation: $(s-a)/4=(s-b)/3=(s-c)/2$ , from this I'm supposed to get a,b and c (the sides of a triangle) in terms of s.. If I substitute $s=(a+b+c)/2$ in the given system of equations I get ...
0
votes
3answers
26 views

$4 \times 4$ matrix and homogeneous system of equations.

I have the following question here: Let $A$ be a $4 \times 4$ matrix such that $x=\begin{matrix}[-4\ 0 \ 2 \ -8]^T \end{matrix}$ is a solution to the homogeneous system of linear equations $Ax=0$. ...
1
vote
1answer
28 views

Convert this sum to normal expression

If I have a sum like this: $$2\sum_{i=0}^{n-1}3^i(3^{n-i}-1)$$ How do I convert it so that I can lose the sum. For example if it was $$\sum_{i=0}^{n}n$$ then the result would be $$\frac{n(n-1)}{2}$...
1
vote
0answers
21 views

Solution of a typical equation with surds power

I was attempting to find a solution for the equation $1 + 12^\sqrt{x} = 9^\sqrt{x} + 10^\sqrt{x}$. By the trial and error, I found a solution $ x = 9$. Is there any method to solve these equation?
1
vote
0answers
15 views

Matlab function which will perform the analysis of my system with respect to Control Theory.

$x`(t)=Ax(t)+Bu(t)$ $y`(t)=Cx(t)$ I have three matrices. For example, the matrices are: And using only one Matlab function I would like to get the following information: 1 Eigenvalues of the ...
0
votes
0answers
18 views

A good reference for DAEs

Can anyone recommend a good reference for the topic "Differential-Algebraic Equations" containing index of DAEs, reduction to problems of index 1 or 2 and some exact methods to find their solutions? ...
0
votes
1answer
26 views

Linear system of equations and distinct solutions

I have the following question here: A certain linear system $Ax=b$ consisting of $n$ unknowns has two distinct solutions $x_1$ and $x_2$ with $x_1 \neq x_2$. Which is the following statements is ...
2
votes
0answers
21 views

Statements about a system of equations true/false

I have the following question here: Consider the homogeneous system $Ax=0$ of $m$ equations for $n>m$ unknowns. Which is the following statements is false? $(A)$ $x=0$ is the only solution ...
1
vote
1answer
34 views

Overdetermined linear system?

What should be the conditions on coefficients $a_i$ and $b_i$ such that the following overdetermined linear system of equations has unique solution. $$a_i x+y=b_i$$ where $i=1,2,3...,n$. The system ...
3
votes
1answer
21 views

What are the values of $k$ that males $x_1,x_2$ solutions to the linear system $AX=B$.

Supose that $x_1$ and $x_2$ are solution to the linear system $ AX=B $ , where $B$ is not equal zero then $3x_1-kx_2$ is a solution also if $k = ?$ How to find the value of $A$ ?
0
votes
2answers
48 views

System of ODEs with integral constrains

Can someone point me in a direction to solve this kind of integral constrained system of ODEs. As far as I know, there are no analytic methods that can solve this. So I will resort to numerical ...
0
votes
1answer
40 views

How to solve a system of equations written using XOR? [on hold]

How to solve a bunch of linear equations written like:- AXORBXORC=a BXORC...
1
vote
1answer
33 views

System of three linear equations with unknown constant

I have a linear system with three equations: $$\begin{align} x + y + z &= 3a\\ x + 2y + (a+2)z &= a\\ x - (a+1)y - z &= 0 \end{align}$$ I want to find values for a where the system is ...
3
votes
2answers
47 views

Solving an algebraic exercise using only one variable $x$

This exercise is supposed to be solved using only one though I don't see how would that be possible. Could someone tell how to solve using only one unknown variable $x$? Thank you. Exercise. The ...
1
vote
2answers
31 views

System of differential equation stability, with initial condition

Consider the following system of differential equations: $$ \dot x(t) = 3x(t) - 2y(t) + 3$$ $$\dot y(t) = 2x(t) - 2y(t) - 1$$ (a) Find the steady state of the system and determine its stability. (...
2
votes
1answer
32 views

Simplify the matrix of a linear system knowing that some of the solutions are equal

In order to improve the efficiency of my python program I'm trying to take advantage of some properties of a linear system I need to solve. I have a linear system $Ax = b$ and I know beforehand that ...
0
votes
2answers
35 views

Solve Equation of Motion when gravity is two dimentional

How does one solve the following system of equation for Θ. Only unknown variables are Θ and t. This is the equation of motion when gravity is two dimensional. WolfarmAlpha succeeded to solve but I ...
1
vote
2answers
48 views

Given $n$ equations in cyclic format how to solve the system? [on hold]

If $x_1+x_2+x_3 = c_1$ $x_2+x_3+x_4 = c_2$ $x_3+x_4+x_5 = c_3$ . . $x_{99}+x_{100}+x_1 = c_{99}$ $x_{100}+x_1+x_2 = c_{100}$ $x_i$ denote variables and $c_i$ denote constants. How to ...
4
votes
2answers
138 views

Find elements from xor relations

Alice and Bob are playing a game. Alice has a sequence of positive integers $$a_1,a_2, \ldots, a_N;$$ Bob should find the values of all elements of this sequence. Bob may ask Alice at most $N$ ...
0
votes
0answers
13 views

Characterizing conditions for non-existence, nonuniqueness for a system of equations

Given a noisy, finite-length signal $x \in \mathbb{R}^n$, we can estimate the SNR of this signal via the $M_2 M_4$ estimator: \begin{align*} M_2 = S + N \quad M_4 = k_a S^2 + 6SN + k_w N^2, S \ge 0, ...
-1
votes
2answers
38 views

Solutions to equation system [on hold]

Statement: The equation system \begin{align*} 3x_1-x_2+2x_3&=0\\ x_1-2x_2+4x_3&=-1\\ 2x_1-3x_2+3x_3&=0 \end{align*} has infinitely many solutions. My answer My calculations says that ...
-1
votes
1answer
44 views

Consider the system Ax = 0 [on hold]

Question: Consider the system Ax = 0, where $$A=\begin{bmatrix} 1 & 6 & 2 & 5 &5\\ 1 & 2 & 2 & 1 & 3 \\ 2 &3&4&4&4\\ 2&-1&...
1
vote
0answers
26 views

Showing that the Riemann invariant $\frac{1}{2} (u^2+v^2) + \int \frac{c(p)^2}{p} dp $ is conserved along the characteristic $dy/dx = v/u$

I need to show that the Riemann invariant $R = \frac{1}{2} (u^2+v^2) + \int \frac{c(p)^2}{p} dp $ is conserved along the characteristic $dy/dx = v/u$. My system of equations are: \begin{aligned} (pu)...
0
votes
1answer
23 views

Is this pair of equations impossible to solve for x? $y_1 = x_2 - v^{\pm 1}e^{-x_1}$, or equivalently $(x - y)c^{\exp(-x)} = z$

Original: I'm trying to solve the following for $x_1$ and $x_2$, $$ y_1 = x_2 - v\, e^{-x_1} $$ $$ y_2 = x_1 - \frac{1}{v}\, e^{-x_2} $$ in terms of $y_1$, $y_2$, and $v$, which are known and real, ...
1
vote
1answer
30 views

Rank, nullity and consistency for two matrices

I have this question here which says the following. Let $A$,$B$ be $3 \times 6$ matrices with the following properties. $(i)$ For every b$\epsilon \mathbb{R}^3$, rank$(A)$ $=$ rank$([A|b])$ $(ii)$ ...
0
votes
1answer
31 views

Do I really need to solve 5 nonlinear equations in this Lagrange multiplier problem?

I need to solve the following optimization problem Let $X=\left\{ x_{i}\right\} _{i=1}^{n}$ be an independent sequence of $k$-face die rolls. Where for $j\in\left[k\right]$ we have $p\left(x_{i}=j\...
0
votes
1answer
43 views

Does $\alpha_j-(\Pi \alpha_i)^{1/d}=\beta_j-(\Pi \beta_i)^{1/d} $ force $\alpha_i=\beta_i$?

Let $d>1$, and let $\alpha_1,\dots,\alpha_d,\beta_1,\dots,\beta_d$ be positive real numbers. Is there an easy proof of the following claim: If $\alpha_j-(\Pi_{i=1}^d \alpha_i)^{1/d}=\beta_j-(\...
0
votes
0answers
14 views

3D trilateration with 3 beacons of two different points with the same height

I know that 3 beacons are enough to find a point's position in a 2D region. By beacon, I mean a device that gives the distance from itself to the point (by calculating the intersections of all the ...
0
votes
1answer
29 views

Recommendations for Numerical Analysis book covering specific requirements?

I have a numerical analysis course, Course content is as follows can anyone recommend me a good book or several books which covers these areas. If the book gives an intuitive idea it would be better. ...
4
votes
2answers
46 views

How to solve this system of equations systematically?

This might seem a trivial problem, but I have some trouble in arranging the data. So suppose you are given $f(x,y)=x^2y^2(1+x+2y)$ and you want to find it's critical points. Thus we find $$\frac{\...
-1
votes
1answer
14 views

Equation of a peak diagram

May you please help me how can I extract the equation for this diagram? This is the diagram (Click) I know that the right side is y=2-2x
0
votes
2answers
19 views

$p_0^2 + q_0^2 = 1$ and $-\sin(s) = -p_0\sin(s) + q_0\cos(s)$ $\rightarrow $ $p_0 = -\cos2s, q_0 = -\sin(2s)$

How does solving $p_0^2 + q_0^2 = 1$ and $-\sin(s) = -p_0\sin(s) + q_0\cos(s)$ give $p_0 = -\cos2s $ and $q_0 = -\sin(2s)$? I can clearly see one solution is $p_0=1,q_0=0$ but can't seem to ...
0
votes
2answers
31 views

Solve Ax=b, where A consist of $x^k$, is my method using RREF on augmented matrix valid?

I have Ax=b, $$ \begin{bmatrix} 1 & x & x^2 \\ x & 1 & x \\ x^2 & x & 1 \end{bmatrix} \begin{bmatrix} a \\ b \\ c \end{bmatrix} = \begin{bmatrix} x \\ x^2 \\ x^3 \end{bmatrix} $...
1
vote
2answers
47 views

Systems of differential equations

\begin{array} { c } { \text { Solve the initial value problem } } \\ { \mathbf { x } ^ { \prime } = \left( \begin{array} { c c } { 1 } & { - 5 } \\ { 1 } & { - 3 } \end{array} \right) \mathbf {...
-1
votes
0answers
24 views

Difference between particular solution and general solution? [closed]

I have this linear system: \begin{cases} x + 2y - 4z + 5w = 1,\\ x + 3y +5z = 0,\\ y - 4z - 6w = -13. \end{cases} I am asked to find the particular and general solution of this system. I do not know ...
0
votes
0answers
22 views

find website equation solver get possible value [closed]

i want find website or app (iphone or mac)about equation solver. for example: i want get x,y,z possible value. if x+y+z=15 or x+y=15 or z+y=15 and x,y,z should in 1-81 int range, and get all possible ...
0
votes
0answers
29 views

Solve for parameters of a system of non linear equations that have forms of $0 = e^x + A_1 e^x + A_2 e^{2x} + A_3$

I'm self studying math and came across a problem that I have to solve for parameters of the following equations, $$ 0 = e^{-x} - A_1 - A_2 e^{-x} - A_3e^{-2x} \\ 0 = e^{-2x} - A_1e^{-x} - A_2 - A_3e^{-...
0
votes
2answers
30 views

Solve the following system of equations using Gaussian Elimination Method

Solve the following system of equations using Gaussian Elimination Method $$x+2y+3z=2$$ $$x+y-z=1$$ $$2x+3y+2z=3$$. My Attempt : $$x+2y+3z=2………(1)$$ $$x+y-z=1…………(2)$$ $$2x+3y+2z=3………(3)$$ ...
1
vote
2answers
70 views

System of Trigonomtric Equations

Please Help to solve the following problem :- If, $$\sin(x+y)=a$$ $$\cos(x-y)=b$$ $$a,b\in \Bbb R^+$$ Find $\tan(2x)$ in terms of a and b.
0
votes
0answers
13 views

Defining a system in MatCont where a parameter depends on other parameter value

I'm trying to define a biological system in MatCont but I'm facing the following problem. A parameter $UU$ depends on another parameter $T_S$ in the following way ...
2
votes
1answer
39 views

Is there an elegant or easier way to solve this system of equations?

This is a physics problem that involves an inelastic collision and a system of equations that I want to solve. I know the values of $v_1,m_1,v',\Delta E$ where $v'$ is the velocity of the two objects ...
1
vote
2answers
70 views

Find minimum values of a linear system over $\mathbb N$

I have the following linear equations: \begin{align} p &= 2(a-c)+b-d\\ q &= 2(e-g)+f-h\\ a+c &= f+h\\ b+d &= e+g\\ \end{align} where $p$ and $q$ are known, and $a$, $b$, $c$, $d$, $e$...
-1
votes
1answer
44 views

Find the area using simultaneous equations [closed]

So the question is to find the areas A - G. You are told that the vertical length is 4 and horizontal length is 28 I started making a load of simultaneous equations but found there was too many ...
-1
votes
1answer
39 views

Changing $b$ of $AX =b$ [closed]

Suppose 3 planes of the form $AX=b$ intersect at a unique point. Suppose in this case $b= (1,1,1)$. In case $b$ is changed to $(2,3,4)$ or any other vector, will the planes still intersect at a ...
1
vote
1answer
31 views

Do the following system of equation have a solution in $\mathbb{Z}_{p}$

Consider the equations $5x + 3y = 4$ and $3x + 6y = 1$. I need to find if these equations has a solution in $\mathbb{Z}_{3}$ or $\mathbb{Z}_{7}$. I solved these equations in the usual way and found ...
3
votes
3answers
111 views

How to solve $AX=XB$ for $X$ Matrix?

I have two symmetric $3\times 3$ matrices $A, B$. I am interested in solving the system $$AX= XB$$ Is there a way this is usually done? The matrices are not necessarily non singular.
0
votes
1answer
16 views

Solving an arithmetical progression equation with 2 equations, rational and multiplied progression members

This is the assignment. We have two equations which we should use to get the first member of the arithmetical progression and the step difference d, $$\frac{a_{27}}{a_{5}}=5,\qquad a_{3}\cdot a_{6}=...
0
votes
0answers
19 views

Non-existence of a generic solution to system of nonlinear equations

I have the following system of nonlinear equations: $f_1(x_1,..,x_m,y) =0$ $...$ $f_n(x_1,..,x_m,y) =0$ where $f_i(\cdot)$ is a nonlinear, (infinitely) differentiable equation (but not polynomial),...
2
votes
2answers
48 views

Mixed Mathematical Chemical problem:

How to calculate the concentration of all species present in a solution with ${ 0.3M}\ {NaH_2PO_4}$? The whole truth is that any time that you add any phosphate ion into an aqueous solution, then ...