### 数学代写|线性代数代写linear algebra代考|MATH1014

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等概率论
• Advanced Mathematical Statistics 高等数理统计学
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|线性代数代写linear algebra代考|SYSTEMS OF LINEAR EQUATIONS

A linear equation in the variables $x_1, \ldots, x_n$ is an equation that can be written in the form
$$a_1 x_1+a_2 x_2+\cdots+a_n x_n=b$$
where $b$ and the coefficients $a_1, \ldots, a_n$ are real or complex numbers, usually known in advance. The subscript $n$ may be any positive integer. In textbook examples and exercises, $n$ is normally between 2 and 5 . In real-life problems, $n$ might be 50 or 5000 , or even larger.
The equations
$$4 x_1-5 x_2+2=x_1 \quad \text { and } \quad x_2=2\left(\sqrt{6}-x_1\right)+x_3$$
are both linear because they can be rearranged algebraically as in equation (1):
$$3 x_1-5 x_2=-2 \text { and } 2 x_1+x_2-x_3=2 \sqrt{6}$$
The equations
$$4 x_1-5 x_2=x_1 x_2 \quad \text { and } \quad x_2=2 \sqrt{x_1}-6$$
are not linear because of the presence of $x_1 x_2$ in the first equation and $\sqrt{x_1}$ in the second. A system of linear equations (or a linear system) is a collection of one or more linear equations involving the same variables-say, $x_1, \ldots, x_n$. An example is
$$\begin{array}{r} 2 x_1-x_2+1.5 x_3=8 \ x_1-4 x_3=-7 \end{array}$$ A solution of the system is a list $\left(s_1, s_2, \ldots, s_n\right)$ of numbers that makes each equation a true statement when the values $s_1, \ldots, s_n$ are substituted for $x_1, \ldots, x_n$, respectively. For instance, $(5,6.5,3)$ is a solution of system ( 2 ) because, when these values are substituted in (2) for $x_1, x_2, x_3$, respectively, the equations simplify to $8=8$ and $-7=-7$.

## 数学代写|线性代数代写linear algebra代考|Matrix Notation

The essential information of a linear system can be recorded compactly in a rectangular array called a matrix. Given the system
\begin{aligned} x_1-2 x_2+x_3 & =0 \ 2 x_2-8 x_3 & =8 \ 5 x_1-5 x_3 & =10 \end{aligned}
with the coefficients of each variable aligned in columns, the matrix
$$\left[\begin{array}{rrr} 1 & -2 & 1 \ 0 & 2 & -8 \ 5 & 0 & -5 \end{array}\right]$$
is called the coefficient matrix (or matrix of coefficients) of the system (3), and
$$\left[\begin{array}{rrrr} 1 & -2 & 1 & 0 \ 0 & 2 & -8 & 8 \ 5 & 0 & -5 & 10 \end{array}\right]$$
is called the augmented matrix of the system. (The second row here contains a zero because the second equation could be written as $0 \cdot x_1+2 x_2-8 x_3=8$.) An augmented matrix of a system consists of the coefficient matrix with an added column containing the constants from the right sides of the equations.

The size of a matrix tells how many rows and columns it has. The augmented matrix (4) above has 3 rows and 4 columns and is called a $3 \times 4$ (read “3 by 4 “) matrix. If $m$ and $n$ are positive integers, an $\boldsymbol{m} \times \boldsymbol{n}$ matrix is a rectangular array of numbers with $m$ rows and $n$ columns. (The number of rows always comes first.) Matrix notation will simplify the calculations in the examples that follow.

# 线性代数代考

## 数学代写|线性代数代写linear algebra代考|SYSTEMS OF LINEAR EQUATIONS

$$a_1 x_1+a_2 x_2+\cdots+a_n x_n=b$$

$$4 x_1-5 x_2+2=x_1 \quad \text { and } \quad x_2=2\left(\sqrt{6}-x_1\right)+x_3$$

$$3 x_1-5 x_2=-2 \text { and } 2 x_1+x_2-x_3=2 \sqrt{6}$$

$$4 x_1-5 x_2=x_1 x_2 \quad \text { and } \quad x_2=2 \sqrt{x_1}-6$$

$$2 x_1-x_2+1.5 x_3=8 x_1-4 x_3=-7$$

## 数学代写|线性代数代写linear algebra代考|Matrix Notation

$$x_1-2 x_2+x_3=02 x_2-8 x_3=85 x_1-5 x_3=10$$

$$\left[\begin{array}{llllllll} 1 & -2 & 1 & 0 & 2 & -85 & 0 & -5 \end{array}\right]$$

$$\left[\begin{array}{lllllllllll} 1 & -2 & 1 & 0 & 0 & 2 & -8 & 85 & 0 & -5 & 10 \end{array}\right]$$

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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。