# 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.

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### What is the "lifted system of linear equations"?

I am reading this blog post, where it says Here’s another variant of the same idea. Suppose we want to solve the linear system of equation $(D + uv^\top)x = b$ where $D$ is a diagonal matrix. Then we ...
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### Proving a the distance between Cauchy sequences converges [duplicate]

Assume we have two Cauchy sequences { $x_n$ } and {$y_n$} in the metric space $(X,d)$. Is it true that the sequence {$a_n$}$=d(x_n,y_n)$ is convergent in $\mathbb{R}$? Here is my try:  Since those ...
635 views

### Solving a quadratic equation problem with two variables

This is a post of two three problems regarding the method to solve bivariate quadratic equations. In brief, How does the elimination happen here. Or, how is the elimination used? (Update, I know how ...
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### Optimizing a linear equation with multiple variables

My maths are a bit rusty, so please excuse me if this is too trivial or has been asked before (very likely!) I have a set of 20 liquids, each described by three characteristics (A, B and C). How can ...
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### Find $a + b$, provided $Y=a\bar{X} + b\bar{X}^2, E(Y) = {1 \over p^2}$ where $X \sim \text{Geo}(p), X_1,X_2,\cdots,X_n$ are simple samples from X.

The question asks you to select one of the choices: A) -1 B) 0 C) 1 D) 2 I understand the answer till the calculation of E(Y), $$E(Y)={a \over p} + {b(n+1)-bp \over np^2} = {1 \over p^2}$$ But then ...
1 vote
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### Can one solve this complex linear equation

Suppose the equations are as follows: $$\text{tr}\{AH\}= c$$ where $c \in \mathbb{C}$ and $A$ is a symmetric matrix in $M_{N}(\mathbb{R})$ are both known and $H$ is a Hermitian matrix which looks like:...
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### Given is the system of equations, solve using numerical methods

Given is the system of equations $$-x + 4y + z = -1, \\ -x + y + az = 3, \\ 3x + 2y = 2.$$ (a) Determine the smallest $a \in \mathbb{N}$ such that the system is solvable by the Jacobi and Gauss-...
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### using fsolve to solve non-linear equations in matlab

I'm trying to solve this system equations in matlab ...
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### Using the Laplace transform, solve the system of linear differential equations with constant coefficients

Using the Laplace transform, solve the system of linear differential equations with constant coefficients $y' + z' = t,$ $y'' - z = e^{-t},$ $y(0) = 3,$ $y'(0) = -2,$ $z(0) = 0,$ where $y(t)$...
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