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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写线性代数linear algebra方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写线性代数linear algebra代写方面经验极为丰富，各种代写线性代数linear algebra相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|THE SIMPLEX METHOD

An important application of the use of elementary row operations and pivoting is the Simplex Method for solving linear programming problems. The topic of linear programming (or linear optimization) requires an entire text of its own and it makes use of linear algebra in a big way. This section is meant as a glimpse into this field of study and its connections to linear algebra. To begin, we introduce the terminology for this setting by way of an example.

Example 2.13 The college cafeteria is offering a lunch consisting of two entrees. The first entree contains $16 \mathrm{~g}$ of fat, $20 \mathrm{~g}$ of carbohydrates and $15 \mathrm{~g}$ of protein per unit serving, while the second contains $10 \mathrm{~g}$ of fat, $30 \mathrm{~g}$ of carbohydrates and $17 \mathrm{~g}$ of protein per unit serving. For lunch, Harry must have at least $100 \mathrm{~g}$ of protein, but at most $50 \mathrm{~g}$ of fat and exactly $75 \mathrm{~g}$ of carbohydrates. The first entree costs $\$ 0.45$per serving while the second costs \$0.65 per serving. How many servings of each entree should Harry take so as to meet his nutritional needs and spend the least amount of money.that we wish to determine in this problem, namely the number of servings of each of the two entrees. Let’s call these unknowns $x$ and $y$. The objective function represents the quantity $z$ that is being optimized (maximized or minimized). In our cxample, it is the cost and we wish to minimize it. Mathematically, cost (in dollars) for Harry’s meal is represented by $z=0.45 x+0.65 y$. The constraints of a linear programming problem are the conditions imposed on the unknowns for the particular problem. For instance, in our example, Harry must have at least 100 grams of protein, i.e. the amount of protein must be $\geq 100$. Each of the two entrees will contribute to the total protein depending on how many servings of each are eaten and mathematically this condition translates into $15 x+17 y \geq 100$. Harry cannot have more than 50 grams of fat becomes $16 x+10 y \leq 50$ and exactly 75 grams of carbohydrates becomes $20 x+30 y=75$. There is also implicit in this problem a positivity constraint, namely that the number of servings must be positive numbers (and perhaps even integers, but we won’t concern ourselves with this for the sake of simplicity), i.e. $x, y \geq 0$.

## 数学代写|线性代数代写linear algebra代考|INVERSE OF A MATRIX

If $a$ is a non-zero real number, then the multiplicative inverse of $a$ is $1 / a$ since $a(1 / a)=$ $1=(1 / a) a$. Note for a real number to have a multiplicative inverse it must be nonzero. We now investigate the existence of multiplicative inverses for matrices using matrix multiplication. We will see that they do not always exist, indeed for more than just the zero matrix. However, in the case that the inverse does exist, we can conclude a number of seemingly unrelated equivalent conditions for its existence. This theorem which we will derive slowly for the remainder of the chapter is the second goal of this chapter. We also give a systematic way to find the inverse of a matrix when it exists.
Definition $2.12$ Let $A$ be a square matrix. $B$ is the inverse of $A$ if $A B=I=B A$. When $A$ has an inverse we say that $A$ is invertible (or non-singular). Otherwise, we say $A$ is non-invertible (or singular).

Note that $A$ must be a square matrix in order for both products $A B$ and $B A$ to be possible.
Example 2.24 The inverse of $\left[\begin{array}{ll}2 & 1 \ 1 & 1\end{array}\right]$ is $\left[\begin{array}{rr}1 & -1 \ -1 & 2\end{array}\right]$ since
$$\left[\begin{array}{ll} 2 & 1 \ 1 & 1 \end{array}\right]\left[\begin{array}{rr} 1 & -1 \ -1 & 2 \end{array}\right]=\left[\begin{array}{ll} 1 & 0 \ 0 & 1 \end{array}\right]=\left[\begin{array}{rr} 1 & -1 \ -1 & 2 \end{array}\right]\left[\begin{array}{ll} 2 & 1 \ 1 & 1 \end{array}\right] \text {. }$$
A number of remarks are in order here.

• ‘l’he inverse of $A$ is necessarily square and of the same dimensions as $A$.
• ‘T’he inverse of a matrix does not always exists. ‘lake the case of $A-0_{n n}$; it has no inverse because for all matrices $B, A B=0_{n n} \neq I_n$. In addition certain nonzero matrices have no inverse. For instance, $A=\left[\begin{array}{ll}1 & 0 \ 0 & 0\end{array}\right]$ (similar argument). In fact, one of our goals is to determine which matrices do have an inverse.

# 线性代数代考

## 数学代写|线性代数代写linear algebra代考|THE SIMPLEX METHOD

.

\left[\begin{array}{ll}
2 & 1 \
1 & 1
\end{array}\right]\left[\begin{array}{rr}
1 & -1 \
-1 & 2
\end{array}\right]=\left[\begin{array}{ll}
1 & 0 \
0 & 1
\end{array}\right]=\left[\begin{array}{rr}
1 & -1 \
-1 & 2
\end{array}\right]\left[\begin{array}{ll}
2 & 1 \
1 & 1
\end{array}\right] \text {. }


• ‘l’he $A$的逆一定是方阵，与$A$的维数相同。
• ‘T’he逆矩阵并不总是存在。以$A-0_{n n}$为例;它没有逆，因为对于所有矩阵$B, A B=0_{n n} \neq I_n$。另外，某些非零矩阵没有逆矩阵。例如，$A=\left[\begin{array}{ll}1 & 0 \ 0 & 0\end{array}\right]$(类似的参数)。事实上，我们的目标之一是确定哪些矩阵有逆。

## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师