## 数学代写|离散数学作业代写discrete mathematics代考|MATH200

2022年9月30日

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## 数学代写|离散数学作业代写discrete mathematics代考|Matrix Theory

A matrix is a rectangular array of numbers that consists of horizontal rows and vertical columns. A matrix with $m$ rows and $n$ columns is termed an $m \times n$ matrix, where $m$ and $n$ are its dimensions. A matrix with an equal number of rows and columns (e.g. $n$ rows and $n$ columns) is termed a square matrix. Figure $8.1$ is an example of a square matrix with four rows and four columns.

The entry in the $i$ th row and the $j$ th column of a matrix $\mathrm{A}$ is denoted by $\mathrm{A}[i, j]$, $\mathrm{A}{i, j}$, or $a{\mathrm{ij}}$, and the matrix A may be denoted by the formula for its $(i, j)$ th entry: i.e. $\left(a_{\mathrm{ij}}\right)$ where $i$ ranges from 1 to $m$ and $j$ ranges from 1 to $n$.

An $m \times 1$ matrix is termed a column vector, and a $1 \times n$ matrix is termed a row vector. Any row or column of a $m \times n$ matrix determines a row or column vector which is obtained by removing the other rows (respectively columns) from the matrix. For example, the row vector $(11,-5,5,3)$ is obtained from the matrix example by removing rows 1,2 and 4 of the matrix.

Two matrices $\mathrm{A}$ and $\mathrm{B}$ are equal if they are both of the same dimensions, and if $a_{i j}=b_{i j}$ for each $i=1,2, \ldots, m$ and each $j=1,2, \ldots n$.

Matrices be added or multiplied (provided certain conditions are satisfied). There are identity matrices under the addition and multiplication binary operations such that the addition of the (additive) identity matrix to any matrix $\mathrm{A}$ yields $\mathrm{A}$ and similarly for the multiplicative identity. Square matrices have inverses (provided that their determinant is non-zero), and every square matrix satisfies its characteristic polynomial.

It is possible to consider matrices with infinite rows and columns, and although it is not possible to write down such matrices explicitly it is still possible to add, subtract and multiply by a scalar provided there is a well-defined entry in each $(i, j)$ th element of the matrix.

Matrices are an example of an algebraic structure known as an algebra. Chapter 6 discussed several algebraic structures such as groups, rings, fields and vector spaces.

## 数学代写|离散数学作业代写discrete mathematics代考|Two Two Matrices

Matrices arose in practice as a means of solving a set of linear equations. One of the earliest examples of their use is in a Chinese text dating from between $300 B C$ and $200 \mathrm{AD}$. The Chinese text showed how matrices could be employed to solve simultaneous equations. Consider the set of equations:
\begin{aligned} &a x+b y=r \ &c x+d y=s \end{aligned}

Then, the coefficients of the linear equations in $x$ and $y$ above may be represented by the matrix $\mathrm{A}$, where $\mathrm{A}$ is given by
$$\mathrm{A}=\left(\begin{array}{ll} a & b \ c & d \end{array}\right) .$$
The linear equations may be represented as the multiplication of the matrix A and a vector $x$ resulting in a vector $v$ :
$$A x=v .$$
The matrix representation of the linear equations and its solution are as follows:
$$\left(\begin{array}{ll} a & b \ c & d \end{array}\right)\left(\begin{array}{l} x \ y \end{array}\right)=\left(\begin{array}{l} r \ s \end{array}\right) .$$
The vector $\mathrm{x}$ may be calculated by determining the inverse of the matrix $\mathrm{A}$ (provided that its inverse exists). The vector $x$ is then given by
$$x=A^{-1} v .$$
The solution to the set of linear equations is then given by
$$\left(\begin{array}{l} x \ y \end{array}\right)=\left(\begin{array}{ll} a & b \ c & d \end{array}\right)^{-1}\left(\begin{array}{l} r \ s \end{array}\right) .$$

# 离散数学代写

## 数学代写|离散数学作业代写离散数学代考|矩阵论

$i$ 第Th行和 $j$ 矩阵的第Th列 $\mathrm{A}$ 表示为 $\mathrm{A}[i, j]$， $\mathrm{A}{i, j}$，或 $a{\mathrm{ij}}$，矩阵A可以用its的公式表示 $(i, j)$ Th条目:即。 $\left(a_{\mathrm{ij}}\right)$ 哪里 $i$ 取值范围为1 ～ $m$ 和 $j$ 取值范围为1 ～ $n$.

$m \times 1$矩阵被称为列向量，$1 \times n$矩阵被称为行向量。$m \times n$矩阵的任何行或列都确定一个行或列向量，该向量是通过从矩阵中删除其他行(分别为列)获得的。例如，行向量$(11,-5,5,3)$是通过删除矩阵的第1行、第2行和第4行从矩阵示例中获得的

## 数学代写|离散数学作业代写离散数学代考|Two Two Matrices

\begin{aligned} &a x+b y=r \ &c x+d y=s \end{aligned}

$$\mathrm{A}=\left(\begin{array}{ll} a & b \ c & d \end{array}\right) .$$线性方程可以表示为矩阵A与一个向量的乘法 $x$ 得到一个向量 $v$ :
$$A x=v .$$线性方程的矩阵表示及其解如下:
$$\left(\begin{array}{ll} a & b \ c & d \end{array}\right)\left(\begin{array}{l} x \ y \end{array}\right)=\left(\begin{array}{l} r \ s \end{array}\right) .$$

## 有限元方法代写

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## 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。