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# 数学代写|离散数学代写Discrete Mathematics代考|MTH315 Matrix Inversion

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## 数学代写|离散数学代写Discrete Mathematics代考|Matrix Inversion

A square matrix $\boldsymbol{A}$ is said to be invertible if there exists a square matrix $\boldsymbol{B}$ such that
$$A B=B A=I \rightarrow B=A^{-1} \& A=B^{-1}$$
where the matrix $B$ is called the inverse of the matrix $A$ and denoted by $A^{-1}$. If $B$ is the inverse of $\boldsymbol{A}$, then $\boldsymbol{A}$ is the inverse of $\boldsymbol{B}$. A square matrix that is not invertible is called singular. Note that if a matrix is not square, then it has no inverse. In addition, a product of invertible matrices is always invertible, and the inverse of the product is the product of the inverses in the reverse order, that is, we have $(A B)^{-1}=B^{-1} A^{-1}$. The inverse of the matrix $A$ plays much the same role in matrix algebra that the reciprocal of a number plays in the arithmetic of real numbers.

An effective method to find the inverse of a matrix is to employ the elementary row operations. The elementary row operations consist of the following suboperations:

• Interchange two rows.
• Multiply all entries in a row by a nonzero number.
• Add a multiple of a row to another row.

## 数学代写|离散数学代写Discrete Mathematics代考|Matrix Inversion

A square matrix $\boldsymbol{A}$ is said to be invertible if there exists a square matrix $\boldsymbol{B}$ such that
$$A B=B A=I \rightarrow B=A^{-1} \& A=B^{-1}$$
where the matrix $B$ is called the inverse of the matrix $A$ and denoted by $A^{-1}$. If $B$ is the inverse of $\boldsymbol{A}$, then $\boldsymbol{A}$ is the inverse of $\boldsymbol{B}$. A square matrix that is not invertible is called singular. Note that if a matrix is not square, then it has no inverse. In addition, a product of invertible matrices is always invertible, and the inverse of the product is the product of the inverses in the reverse order, that is, we have $(A B)^{-1}=B^{-1} A^{-1}$. The inverse of the matrix $A$ plays much the same role in matrix algebra that the reciprocal of a number plays in the arithmetic of real numbers.

An effective method to find the inverse of a matrix is to employ the elementary row operations. The elementary row operations consist of the following suboperations:

• Interchange two rows.
• Multiply all entries in a row by a nonzero number.
• Add a multiple of a row to another row.

## 数学代写|离散数学代写Discrete Mathematics代考|Matrix Inversion

$$A B=B A=I \rightarrow B=A^{-1} \& A=B^{-1}$$

• 交换两行。
• 将一行中的所有条目乘以一个非零数。
• 将一行的倍数添加到另一行。

## 数学代写|离散数学代写Discrete Mathematics代考|Matrix Inversion

$$A B=B A=I \rightarrow B=A^{-1} \& A=B^{-1}$$

• 交换两行。
• 将一行中的所有条目乘以一个非零数。
• 将一行的倍数添加到另一行。

## 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。