# Tagged Questions

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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### Why equations are called independent and dependent?

I am not sure if I am trying to know everything to detail, but why for example two equations are called independent if they have only single solution? On what they think about when they say single ...
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### System of differential equations

We suppose that we have a system of differential equations $$\left\{\begin{matrix} L_1 y=0\\ L_2 y=0 \end{matrix}\right. \tag 1$$ where there order of $L_1 y$ is $n$ and the order of $L_2 y$ is $m$...
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### Find the equation of the line for this impilcit differential

Here is the question. A set of points in this graph that satisfies the the equation of the line tangent to this curve at the point (0,4) So I started by finding the derivative But I am not ...
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### Solving a nonlinear algebraic system representing the equilibrium of a system of ODEs

Given the following system: $$a_1+(a_3+a_4)V-a_5WX = 0 \\ (a_7+a_4)Y-a_6WZ = 0 \\ a_2-W(a_4+a_5X+a_6Z)+(a_3+a_8)V+a_7Y = 0 \\ a_5WX-(a_3+a_8+a_4)V = 0 \\ a_6WZ-(a_7+a_4)Y = 0$$ where $a_1$ to $a_8$...
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### Questions regarding the basis for the solution set of a system.

I've seen a couple of examples like this but there's a thing I don't understand. I have to determine a basis for the solution set of the system: $$x-y-7=0\\ 2x-y+7=0$$ So based on the examples, ...
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### The Rank of the Matrix Given its Solution Space

$\quad$ Let $A$ be a $5$x$4$ matrix.There exists a vector(column) $B=[0,1,2,3,4]^{T}$ such that the solution space of $AX=B$ is $[1+2s,2+3s,3+4s,4+5s]^{T}$where $s \in \mathbb R$. Find the rank of the ...
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### Possible values of $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$ given $x+y+z=1$

Given $x,y,z$ are real numbers and $x+y+z=1$ and $x$ is not equal to $z$, if ${1\over x} + {1\over y} + {1\over z} = m$, which of the following values of $m$ are possible? (A) 1 (B) 2 (C) 3 (D)...
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### Solving Currents in Electrical Networks for Graph Theory

I need help trying to solve this question, been cracking my head for the whole week and my professor said he used an online solver but in exams we have to solve by hand! Given these 8 equations, we ...
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### System of equations based question in matrix form

If $\begin{bmatrix}1^2&2^2&3^2\\2^2&3^2&4^2\\3^2&4^2&5^2\\4^2&5^2&6^2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}1\\4\\10\\\lambda\end{bmatrix}$,...
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### Number of solutions in a system for values a and b

In general, if you are given a system with some a and b like $x + y + z = a$ $x + 2z= b$ $x + ay + z=b$ And asked to find the values a and b such that the system has no solution, infinitely many ...
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### Square of a matrix as coefficients for a system of linear equations

small question I'm having a disagreement with a classmate over - it's a question in a book: Let $A$ be a square matrix $n \times n$ Prove or disprove: If the system $A\underline{x}=\underline{b}$ ...
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### System of n equations

I had a task which was solved (here you can find it: System of two equations with two different non-linear variables). I looked at it wider and I'm wondering now what if there would be system of $n$ ...
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### How to show a certain integer solution does not exist for a system of linear equations?

I'm having some trouble with the following problem: Considering an independent system of linear equations in $x$ and $y$ with integer coefficients ax + by = c_1\\ cx + dy = c_2. \end{...