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.

2,041 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
225 views

How can I guarantee the existence of a solution to this quadratic system of equations?

I have $n$ real quadratic equations and $n$ real variables, $x_i$, of the following form: $$\sum_{i\neq j} a_{ijk}x_ix_j+\sum_ib_{ik}x_i+c_k=0 \ \forall k$$ for $i,j,k\in\{1,\dots n\}$; all ...
• 274
275 views

• 7,969
113 views

• 85
39 views

• 268k
99 views

Solving Vandermonde-style set of simultaneous equations

Imagine there's a set of ordered coefficients $\lambda_1>\lambda_2>\ldots>\lambda_n>0$ which I don't know. However, I know the set of relations $$\sum_{i=1}^n\lambda_i^k(-1)^{i+1}=a_k$$ ...
• 201
122 views

6 linear PDE for only 3 unknowns?

Let $x \in (0,L)$, $t \in (0,T)$, and let $u_0 = u_0(x) \in \mathbb{R}^3$, $g=g(t) \in \mathbb{R}^3$, $P = P(x,t) \in \mathbb{R}^3$ and $Q = Q(x,t) \in \mathbb{R}^3$ be continuously differentiable ...
• 469
130 views

What is the probability of exactly one negative solution in a Fibonacci system of equations?

The Fibonacci numbers denoted by $F_i$ for $i\ge1$ are $$1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,\cdots$$ where they satisfy the property $F_{i+2}=F_{i+1}+F_i$. I have listed the first $15$ ...
• 27.1k
316 views

Reducing to reduced echelon form in linear algebra seems to do so many useful things - what gives? Why?

What's the underlying thing about reducing a matrix to reduced echelon form that solves so many things for us? Some determinations that can be from reducing to reduced echelon form: Testing linear ...
• 1,957
176 views

Probability to obtain no solutions for a linear system

Suppose $Ax=b$ is a linear system and A is a $n \times n$ matrix and vector $b \neq 0$. Suppose all numbers $a_i$ in $A$ and $b_i$ in $b$ belong to $\mathbb{Z}$ and suppose they are in a fixed range ...
• 51
187 views

• 144
223 views

Equivalence of system of nonlinear equations

Let $A\in\mathbb{R}^{n\times n}$ be a positive semidefinite matrix, $b\in\mathbb{R}^n$, $k>0$, and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ be a positive function. Consider the system of nonlinear ...
• 1,016
171 views

System of non-linear ODE's

do you have any suggestions to solve analytically the Non-linear ODE system $\dot x=18 x^2 y-3p x^2+6p xy$ $\dot y=18 x^2 y-6p xy$ where $p$ is a real constant. Thank you very much cheers
130 views

System of equations over $\mathbb{Z}_{2^n}$ with conditions

During my research I stumbled upon this system over $\mathbb{Z}_{2^n}$. Let $k=2^{n-1}-1$ then the system looks like \begin{equation*} \begin{cases} x_1+2^{n-1}=d_k +x_k \\ x_2+2^{n-1}=d_1+x_1 \\ ...
• 67