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# 数学代考|线性代数代写Linear algebra代考|MATH7000 Linear Equations and Electrical Networks

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## 数学代考|线性代数代写LINEAR ALGEBRA代考|Linear Equations and Electrical Networks

Current flow in a simple electrical network can be described by a system of linear equations. A voltage source such as a battery forces a current of electrons to flow through the network. When the current passes through a resistor (such as a lightbulb or motor), some of the voltage is “used up”; by Ohm’s law, this “voltage drop” across a resistor is given by
$$V=R I$$
where the voltage $V$ is measured in volts, the resistance $R$ in ohms (denoted by $\Omega$ ), and the current flow $I$ in amperes (amps, for short).

The network in Figure 1 contains three closed loops. The currents flowing in loops 1,2 , and 3 are denoted by $I_{1}, I_{2}$, and $I_{3}$, respectively. The designated directions of such loop currents are arbitrary. If a current turns out to be negative, then the actual direction of current flow is opposite to that chosen in the figure. If the current direction shown is away from the positive (longer) side of a battery $(-1)$ around to the negative (shorter) side, the voltage is positive; otherwise, the voltage is negative.
Current flow in a loop is governed by the following rule.

## 数学代考|线性代数代写LINEAR ALGEBRA代考|Difference Equations

In many fields such as ecology, economics, and engineering, a need arises to model mathematically a dynamic system that changes over time. Several features of the system are each measured at discrete time intervals, producing a sequence of vectors $\mathbf{x}{0}, \mathbf{x}{1}$, $\mathbf{x}{2}, \ldots$. The entries in $\mathbf{x}{k}$ provide information about the state of the system at the time of the $k$ th measurement.
If there is a matrix $A$ such that $\mathbf{x}{1}=A \mathbf{x}{0}, \mathbf{x}{2}=A \mathbf{x}{1}$, and, in general,
$$\mathbf{x}{k+1}=A \mathbf{x}{k} \quad \text { for } k=0,1,2, \ldots$$
then (5) is called a linear difference equation (or recurrence relation). Given such an equation, one can compute $\mathbf{x}{1}, \mathbf{x}{2}$, and so on, provided $\mathbf{x}{0}$ is known. Sections $4.8$ and $4.9$, and several sections in Chapter 5 , will develop formulas for $\mathbf{x}{k}$ and describe what can happen to $\mathbf{x}_{k}$ as $k$ increases indefinitely. The discussion below illustrates how a difference equation might arise.

A subject of interest to demographers is the movement of populations or groups of people from one region to another. The simple model here considers the changes in the population of a certain city and its surrounding suburbs over a period of years.

Fix an initial year-say, 2014- and denote the populations of the city and suburbs that year by $r_{0}$ and $s_{0}$, respectively. Let $\mathbf{x}_{0}$ be the population vector

For 2015 and subsequent years, denote the populations of the city and suburbs by the vectors
$$\mathbf{x}{1}=\left[\begin{array}{l} r{1} \ s_{1} \end{array}\right], \quad \mathbf{x}{2}=\left[\begin{array}{l} r{2} \ s_{2} \end{array}\right], \quad \mathbf{x}{3}=\left[\begin{array}{l} r{3} \ s_{3} \end{array}\right], \ldots$$
Our goal is to describe mathematically how these vectors might be related.

## 数学代考|线性代数代写LINEAR ALGEBRA代考|Linear Equations and Electrical Networks

$$V=R I$$

## 数学代考|线性代数代写LINEAR ALGEBRA代考|Difference Equations

$$\mathbf{x} k+1=A \mathbf{x} k \quad \text { for } k=0,1,2, \ldots$$

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。